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• https://classificationoffinitesimplegroups.wordpress.com/ — found via User

  Classification of finite simple groups

  Much (if not all) of the proofs were publishied last century, to old for me to got an overview of the timeline on my own. Also I did not waste much time i…

• http://mathoverflow.net/q/34424 — found via Mwmbl

  gr.group theory - Number of finite simple groups of given order …

  $\begingroup$ Here's a pedantic comment: my understanding (which might be wrong!) was that the final flourish of the classification was a computation whic…

  gr.group theory - maximal subgroups of finite simple groups - Ma… 2 Answers 2 Prop: If $G$ is a finite simple group, then a maximal subgroup of $G$ is trivial or has composite order Proof: A maximal subgroup of $G$ bein…
  gr.group theory - Generating finite simple groups with $2$ eleme… The answer to your question is yes. Moreover, if you pick two random elements from a finite simple group, then they generate the whole group with probabil…
  finite groups - Applications of fusion systems - MathOverflow What are the applications of theory of fusion systems to finite group theory or representation theory of finite groups? More concretely, is there any imp…

• https://en.wikipedia.org/wiki/List_of_finite_simple_groups — found via Wikipedia

  List of finite simple groups

  the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie

  Group of Lie type group with values in a finite field. The important collection of finite simple groups of Lie type make up most of the groups in the classification of

• https://terrytao.wordpress.com/tag/finite-simple-groups/ — found via Mwmbl

  finite simple groups | What's new

  Emmanuel Breuillard, Ben Green, Bob Guralnick, and I have just uploaded to the arXiv our joint paper “Expansion in finite simple groups of Lie type“. Thi…

• http://www.youtube.com/watch?gl=GB&hl=en-GB&v=BipvGD-LCjU — found via Mwmbl

  Finite Simple Group (of Order Two) - YouTube

• http://arxiv.org/abs/0808.0622 — found via Mwmbl

  [0808.0622] On the Shortest Identity in Finite Simple Groups of …

  Title:On the Shortest Identity in Finite Simple Groups of Lie Type Abstract:We prove that the length of the shortest identity in a finite simple group of…

  [1312.2311v1] Simple groups of automorphisms of trees determined… Abstract:We introduce the notion of the $k$-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. …
  [1409.7518v1] Which finite simple groups are unit groups? Title:Which finite simple groups are unit groups? Abstract:We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is i…
  [1009.6183v1] Simple groups admit Beauville structures Title:Simple groups admit Beauville structures Abstract:We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups oth…
  [1005.1858] Growth in finite simple groups of Lie type of bounde… Title:Growth in finite simple groups of Lie type of bounded rank Abstract:We prove that if L is a finite simple group of Lie type and A a symmetric set o…
  [1102.3021v1] Spectra of finite symplectic and orthogonal groups Title:Spectra of finite symplectic and orthogonal groups Abstract:The spectra of a finite group is the set of its element orders. We obtain an arithmetic…
  [2406.17794] A characterization of some finite simple groups by … Title:A characterization of some finite simple groups by their character codegrees Abstract:For a finite group $G$ and an irreducible complex character $…
  [0712.4069] The Bogomolov multiplier of finite simple groups Title:The Bogomolov multiplier of finite simple groups Abstract:The subgroup of the Schur multiplier of a finite group G consisting of all cohomology cla…
  [1907.10828] Short presentations of finite simple groups Title:Short presentations of finite simple groups Abstract:Guralnick, Kantor, Kassabov and Lubotzky (J. Eur. Math. Soc. 13.2, 2011, 391-458) [GKKL] give …
  [1312.2311] Simple groups of automorphisms of trees determined b… Abstract:We introduce the notion of the $k$-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. …
  [1312.2311v2] Simple groups of automorphisms of trees determined… Abstract:We introduce the notion of the $k$-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. …
  [2003.00755v1] On the p-width of finite simple groups Title:On the p-width of finite simple groups Abstract:In this paper we measure how efficiently a finite simple group $G$ is generated by its elements of …
  [1001.4556] Growth in finite simple groups of Lie type Title:Growth in finite simple groups of Lie type Abstract: We prove that if L is a finite simple group of Lie type and A a symmetric set of generators of…
  [1003.5611] Lie theory of finite simple groups and the Roth prop… Title:Lie theory of finite simple groups and the Roth property Abstract:In noncommutative geometry a `Lie algebra' or bidirectional bicovariant different…
  [2003.00755v2] On the p-width of finite simple groups Title:On the p-width of finite simple groups Abstract:In this paper we measure how efficiently a finite simple group $G$ is generated by its elements of …
  [1001.5069] Expansion properties of finite simple groups Title:Expansion properties of finite simple groups Abstract: We prove that if G is SL_2(F) or PSL_2(F), where F is a finite field, and A is a set of gene…
  [1402.0341] Metric ultraproducts of finite simple groups Title:Metric ultraproducts of finite simple groups Abstract:Some new results on metric ultraproducts of finite simple groups are presented. Suppose that …
  [1003.5611v2] Lie theory of finite simple groups and the Roth pr… Title:Lie theory of finite simple groups and the Roth property Abstract:We apply noncommutative differential geometry to finite nonabelian simple groups …
  [1003.5611v4] Lie theory of finite simple groups and the Roth pr… Title:Lie theory of finite simple groups and the Roth property Abstract:In noncommutative geometry a `Lie algebra' or bidirectional bicovariant different…
  [2210.14689v1] Non-abelian simple groups which occur as the type… Title:Non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension Abstract:We determine the finite non-abelian s…
  [1003.5611v3] Lie theory of finite simple groups and the Roth pr… Title:Lie theory of finite simple groups and the Roth property Abstract:In noncommutative geometry a `Lie algebra' or bidirectional bicovariant different…
  [1603.04717] Generation of finite simple groups by an involution… arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features …
  [2210.14689v2] Non-abelian simple groups which occur as the type… Title:Non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension Abstract:We determine the finite non-abelian s…
  [2101.09071] Finitely presented simple groups and measure equiva… Title:Finitely presented simple groups and measure equivalence Abstract:We exhibit explicit infinite families of finitely presented, Kazhdan, simple grou…
  [0808.0622v2] On the Shortest Identity in Finite Simple Groups o… Title:On the Shortest Identity in Finite Simple Groups of Lie Type Abstract:We prove that the length of the shortest identity in a finite simple group of…
  [2105.03614] Simple groups with Brauer trees of principal blocks… Title:Simple groups with Brauer trees of principal blocks in the shape of a star Abstract:We have found a list of finite simple groups with cyclic Sylow …
  [1603.04717v1] Generation of finite simple groups by an involuti… arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features …
  [1603.04717v2] Generation of finite simple groups by an involuti… arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features …
  [1003.5611v1] Lie theory of finite simple groups and the general… Abstract:We apply a recent approach to noncommutative differential geometry on finite groups to the case of finite nonabelian simple groups and similar g…
  [1811.05343] Totally orthogonal finite simple groups Title:Totally orthogonal finite simple groups Abstract:We prove that if $G$ is a finite simple group, then all irreducible complex representations of $G$…
  [1901.00836] Word Maps in Finite Simple Groups Title:Word Maps in Finite Simple Groups Abstract:Elements of the free group define interesting maps, known as word maps, on groups. It was previously obs…
  [1911.02117] Simple groups with infinite verbal width and the sa… Abstract:In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abeli…
  [1309.1975] Expansion in finite simple groups of Lie type Abstract: We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the B…
  [1409.7518] Which finite simple groups are unit groups? Title:Which finite simple groups are unit groups? Abstract:We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is i…
  [1707.02057] Simple groups of Morley rank 5 are bad Abstract: By exploiting the geometry of involutions in $N_\circ^\circ$-groups of finite Morley rank, we show that any simple group of Morley rank $5$ is a…
  [2207.08788v7] Finite simple permutation groups acting with fixi… Abstract: Motivated by the theory of Riemann surfaces and specifically the significance of Weierstrass points, we classify all finite simple groups that h…
  [1107.4130] Frobenius' result on simple groups of order (p^3-p)/2 Title:Frobenius' result on simple groups of order (p^3-p)/2 Abstract:The complete list of pairs of non-isomorphic finite simple groups having the same or…
  [1104.1277] Classification of some countable descendant-homogene… Title:Classification of some countable descendant-homogeneous digraphs Abstract:For finite q, we classify the countable, descendant-homogeneous digraphs …
  [1703.07905] A finite simple group is CCA if and only if it has … Title:A finite simple group is CCA if and only if it has no element of order four Abstract:A Cayley graph for a group $G$ is CCA if every automorphism of…
  [1201.0272v2] Finite simple additively idempotent semirings Title:Finite simple additively idempotent semirings Abstract:Since for the classification of finite (congruence-)simple semirings it remains to classify …
  [1201.0272v1] Finite simple additively idempotent semirings Title:Finite simple additively idempotent semirings Abstract:Since for the classification of finite (congruence-)simple semirings it remains to classify …
  [1201.0272] Finite simple additively idempotent semirings Title:Finite simple additively idempotent semirings Abstract:Since for the classification of finite (congruence-)simple semirings it remains to classify …
  [2204.00775] Class Numbers, Cyclic Simple Groups and Arithmetic Title:Class Numbers, Cyclic Simple Groups and Arithmetic Abstract:Here we initiate a program to study relationships between finite groups and arithmetic-…
  [1102.3021] Spectra of finite symplectic and orthogonal groups Title:Spectra of finite symplectic and orthogonal groups Abstract:The spectra of a finite group is the set of its element orders. We obtain an arithmetic…
  [1807.03879] Expansion in simple groups Title:Expansion in simple groups Abstract:Two short seminal papers of Margulis used Kazhdan's property $(T)$ to give, on the one hand, explicit construct…
  [1710.07183] Algorithms determining finite simple images of fini… Abstract:We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary …
  [2210.14689] Non-abelian simple groups which occur as the type o… Abstract: We determine the finite non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension. In the language of…
  [1608.00461] Chabauty limits of simple groups acting on trees Title:Chabauty limits of simple groups acting on trees Abstract:Let $T$ be a locally finite tree without vertices of degree $1$. We show that among the c…
  [2312.15745] Finite almost simple groups whose holomorph contain… Abstract:In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In …
  [1001.0020] Classification of integrable hydrodynamic chains Title:Classification of integrable hydrodynamic chains Abstract: Using the method of hydrodynamic reductions, we find all integrable infinite (1+1)-dimen…
  [1011.1057] Structure of finite nilspaces and inverse theorems f… Title:Structure of finite nilspaces and inverse theorems for the Gowers norms in bounded exponent groups Abstract:A result of the author shows that the b…
  [1311.6733] Large subgroups of simple groups Title:Large subgroups of simple groups Abstract:Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies…
  [1311.6733v1] Large subgroups of simple groups Title:Large subgroups of simple groups Abstract:Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies…
  [1311.6733v2] Large subgroups of simple groups Title:Large subgroups of simple groups Abstract:Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies…
  [1501.00135] Classification of finite simple amenable ${\cal Z}$… arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features …
  [2207.08788] Finite simple permutation groups acting with fixity… Abstract: Motivated by the theory of Riemann surfaces and specifically the significance of Weierstrass points, we classify all finite simple groups that h…
  [1410.6111] On homology of finite topological spaces Title:On homology of finite topological spaces Abstract:We develop a new method to compute the homology groups of finite topological spaces (or equivalen…
  Actions of large finite groups on aspherical manifolds Abstract. In this paper we study actions of finite groups on closed connected aspherical manifolds. Under some assumptions on the outer automorphism grou…
  [1112.3739] Groups of Finite Morley Rank with a Pseudoreflection… Title:Groups of Finite Morley Rank with a Pseudoreflection Action Abstract:In this work, we give two characterisations of the general linear group as a g…
  [1511.08241] Simple groups of dynamical origin Title:Simple groups of dynamical origin Abstract:We associate with every etale groupoid G two normal subgroups S(G) and A(G) of the topological full grou…
  [1009.6183] Simple groups admit Beauville structures Abstract: We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit…
  [1312.7192] Enumeration of finite inverse semigroups Title:Enumeration of finite inverse semigroups Abstract:We give an efficient algorithm for the enumeration up to isomorphism of the inverse semigroups of…
  [0704.0537] Linearisation of finite abelian subgroups of the Cre… Title:Linearisation of finite abelian subgroups of the Cremona group of the plane Abstract: This article gives the proof of results announced in [J. Blan…
  [0903.0180] Classification of continuously transitive circle gro… Title:Classification of continuously transitive circle groups Abstract: Let G be a closed transitive subgroup of Homeo(S^1) which contains a non-constant…
  [2012.08400] Constructing finite simple solutions of the Yang-Ba… Abstract:We study involutive non-degenerate set-theoretic solutions (X,r) of the Yang-Baxter equation on a finite set X. The emphasis is on the case wher…
  [2407.16926] Commuting Involutions in Finite Simple Groups Title:Commuting Involutions in Finite Simple Groups Abstract:We prove that if $G$ is a finite simple group and $x, y \in G$ are involutions, then $|x^G \…
  [0810.2637] Classification of finite-growth general Kac-Moody su… Title:Classification of finite-growth general Kac-Moody superalgebras Abstract: A contragredient Lie superalgebra is a superalgebra defined by a Cartan m…
  [0909.3284] Classification of simple linearly compact n-Lie supe… Title:Classification of simple linearly compact n-Lie superalgebras Abstract: We classify simple linearly compact n-Lie superalgebras with n>2 over a fie…
  [1312.4246] Classification of finite-multiplicity symmetric pairs Title:Classification of finite-multiplicity symmetric pairs Abstract:We give a complete classification of the reductive symmetric pairs (G,H) for which t…
  [math/0511191] Orders of Finite Groups of Matrices Title:Orders of Finite Groups of Matrices Abstract: We present a new proof of a theorem of Schur's determining the least common multiple of the orders of…
  [1610.01219] Actions of finite groups and smooth functions on su… Title:Actions of finite groups and smooth functions on surfaces Abstract:Let $f:M\to \mathbb{R}$ be a Morse function on a smooth closed surface, $V$ be a…
  [2404.17322] Filtered Boolean powers of finite simple non-abelia… Abstract: Let $\mathbf{A}$ be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring). We investigate the Boolean power $\mathbf{D}$ of $\m…
  Filtered Boolean powers of finite simple non-abelian Mal’cev alg… Abstract. Let 𝐀𝐀\mathbf{A}bold_A be a finite simple non-abelian Mal’cev algebra (e.g. a group, loop, ring). We investigate the Boolean power 𝐃𝐃\mathbf{D}…
  [1712.04553v1] MaxDim of some simple groups Title:MaxDim of some simple groups Abstract:MaxDim, along with it relatives m and i, are group invariants analogous to the concept of dimension in vector…
  [0910.5402] New Beauville surfaces and finite simple groups Title:New Beauville surfaces and finite simple groups Abstract:In this paper we construct new Beauville surfaces with group either $\PSL(2,p^e)$, or belo…
  [2401.00638] A class of finite $p$-groups and the normalized uni… Title:A class of finite $p$-groups and the normalized unit groups of group algebras Abstract:Let $p$ be a prime and $\mathbb{F}_p$ be a finite field of $…
  [1712.04553] MaxDim of some simple groups Title:MaxDim of some simple groups Abstract:MaxDim, along with it relatives m and i, are group invariants analogous to the concept of dimension in vector…
  [0706.0790] Free Actions of Finite Groups on $S^n \times S^n$ Title:Free Actions of Finite Groups on $S^n \times S^n$ Abstract: Let $p$ be an odd prime. We construct a non-abelian extension $\Gamma$ of $S^1$ by $Z/p…
  [0810.0568v1] Finite simple groups with narrow prime spectrum Title:Finite simple groups with narrow prime spectrum Abstract: We find the nonabelian finite simple groups with order prime divisors not exceeding 1000.…
  [1010.3528] Combinatorics of finite abelian groups and Weil repr… Title:Combinatorics of finite abelian groups and Weil representations Abstract:The Weil representation of the symplectic group associated to a finite abe…
  [1802.09258] Simple groups of birational transformations in dime… Title:Simple groups of birational transformations in dimension two Abstract:We classify simple groups that act by birational transformations on compact c…
  [2008.02558] Shintani descent, simple groups and spread Title:Shintani descent, simple groups and spread Abstract:The spread of a group $G$, written $s(G)$, is the largest $k$ such that for any nontrivial elem…
  [0810.0568] Finite simple groups with narrow prime spectrum Title:Finite simple groups with narrow prime spectrum Abstract: We find the nonabelian finite simple groups with order prime divisors not exceeding 1000.…
  [2402.02269] The binary actions of simple groups with a single c… Title:The binary actions of simple groups with a single conjugacy class of involutions Abstract:We continue our investigation of binary actions of simple…

• http://pastebin.com/HyKGVbWR — found via Mwmbl

  Finite non-abelian simple groups - Pastebin.com