A Simple Classification of Finite Groups of Order p2q2 [PDF]
Mathematics Interdisciplinary Research, 2018 Suppose G is a group of order p2q2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p2q2 when Q and P are
Aziz Seyyed Hadi +2 more
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Classification of tetravalent $2$-transitive non-normal Cayley graphs of\n finite simple groups [PDF]
Bulletin of the Australian Mathematical Society, 2016 A graph $Γ$ is called $(G, s)$-arc-transitive if $G \le \mathrm{Aut}(Γ)$ is transitive on the set of vertices of $Γ$ and the set of $s$-arcs of $Γ$, where for an integer $s \ge 1$ an $s$-arc of $Γ$ is a sequence of $s+1$ vertices $(v_0,v_1,\ldots,v_s)$ of $Γ$ such that $v_{i-1}$ and $v_i$ are adjacent for $1 \le i \le s$ and $v_{i-1}\ne v_{i+1}$ for $1
Xin Fang, Jie Wang, Sanming Zhou
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Maximal subgroups of finite simple groups: classifications and applications [PDF]
, 2021 This paper surveys what is currently known about the maximal subgroups of the finite simple groups. After briefly introducing the groups themselves, if their maximal subgroups are completely determined then we present this classification. For the remaining finite simple groups our current knowledge is only partial: we describe the state of play, as ...
Colva M. Roney‐Dougal
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Dixon's asymptotic without the classification of finite simple groups [PDF]
Random Structures & Algorithms, 2023 AbstractWithout using the classification of finite simple groups (CFSG), we show that the probability that two random elements of generate a primitive group smaller than is at most . As a corollary we get Dixon's asymptotic expansion for the probability that two random elements of (or ) generate a subgroup containing .
Sean Eberhard
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On groups with chordal power graph, including a classification in the case of finite simple groups [PDF]
Journal of Algebraic Combinatorics, 2023 AbstractWe prove various properties on the structure of groups whose power graph is chordal. Nilpotent groups with this property have been classified by (Electron J Combin 28(3):14, 2021). Here we classify the finite simple groups with chordal power graph, relative to typical number theoretic conditions.
Jendrik Brachter, Eda Kaja
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Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups [PDF]
Episteme, 2021 AbstractIn this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of ...
Joshua Habgood‐Coote +1 more
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On the classification of finite simple groups by the number of involutions [PDF]
Proceedings of the American Mathematical Society, 1979 Simple groups with k involutions, where k ≡ 1 k \equiv 1 (modulo 4), are completely determined.
Marcel Herzog
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A brief history of the classification of the finite simple groups [PDF]
Bulletin of the American Mathematical Society, 2001 We present some highlights of the 110-year project to classify the finite simple groups.
Ronald Solomon
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Afterword to the article “A brief history of the classification of the finite simple groups” [PDF]
Bulletin of the American Mathematical Society, 2018 In this afterword the author discusses his previously published article “A brief history of the classification of the finite simple groups”, which appeared in Bull. Amer. Math. Soc. (N.S) 38 (2001), no. 3, 315–352.
Ron Solomon
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The classification of local m-GCI-group on finite nonabelian simple groups [PDF]
, 2019 Li and Praeger classified finite nonabelian simple groups, it has only one or two fusion classes of any certain value. As a by-product, they classified m-CI-groups, which is critical in the research of Cayley graphs. In the paper, we will consider generalized Cayley graphs. This concept is proposed by Marusic et al.
Xiaomin Zhu, Xu Yang
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