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Factorisations of sporadic simple groups
Journal of Algebra, 2006 A group \(G\) is called factorizable if there exist proper subgroups \(A\) and \(B \) of \(G\) such that \(G=AB\). The factorization is called exact if \(A\cap B=1\) is the trivial group. Recently factorizations of finite groups have attracted attention of mathematicians so that we mention a few research works. \textit{J. Wiegold} and \textit{A.
Michael Giudici
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Commuting involution graphs for sporadic simple groups
Journal of Algebra, 2007 Let \(G\) be a finite group, \(t\in G\) an involution and \(X=t^G\). The commuting involution graph \({\mathcal C}(G,X)\) has \(X\) as its vertex set with two distinct elements of \(X\) joined by an edge whenever they commute in \(G\). A number of authors have studied \({\mathcal C}(G,X)\) for various choices of \(G\) and \(X\), for example, \textit{B.
Bates, C. +3 more
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The admissibility of sporadic simple groups
Journal of Algebra, 2009 A complete mapping of a group \(G\) is a bijection \(\theta\colon G\to G\) for which the mapping \(g\to g\theta(g)\) is also a bijection; \(G\) is admissible if \(G\) admits complete mappings. The Cayley table of a finite group \(G\) is a Latin square, and this Latin square has an orthogonal mate if and only if \(G\) is admissible.
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Regular orbits of sporadic simple groups [PDF]
Journal of Algebra, 2019 Given a finite group $G$ and a faithful irreducible $FG$-module $V$ where $F$ has prime order, does $G$ have a regular orbit on $V$? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2.
Fawcett, Joanna B. +3 more
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On Efficient Presentations of the Groups PSL $(2, m)$ [PDF]
International Journal of Group Theory, 2022 We exhibit presentations of the Von Dyck groups $D(2, 3, m), \ m\ge 3$, in terms of two generators of order $m$ satisfying three relations, one of which is Artin's braid relation. By dropping the relation which fixes the order of the generators we obtain
Orlin Stoytchev
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Upper bounds on the uniform spreads of the sporadic simple groups [PDF]
International Journal of Group Theory, 2019 A finite group $G$ has uniform spread $k$ if there exists a fixed conjugacy class $C$ of elements in $G$ with the property that for any $k$ nontrivial elements $s_1, s_2,ldots,s_k$ in $G$ there exists $yin C$ such that $G = langle s_i,yrangle$ for $
Ali Raza Rahimipour, Yousof Farzaneh
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On homogeneous spaces with finite anti-solvable stabilizers
Comptes Rendus. Mathématique, 2022 We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alternating groups for $n\ne 6$ and all 26 sporadic simple groups. We prove that,
Lucchini Arteche, Giancarlo
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The conjugacy class ranks of $M_{24}$ [PDF]
International Journal of Group Theory, 2017 $M_{24}$ is the largest Mathieu sporadic simple group of order $244 823 040 = 2^{10} {cdot} 3^3 {cdot} 5 {cdot} 7 {cdot} 11 {cdot} 23$ and contains all the other Mathieu sporadic simple groups as subgroups.
Zwelethemba Mpono
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Base sizes for sporadic simple groups [PDF]
Israel Journal of Mathematics, 2010 Let \(G\) be a permutation group acting on a set \(\Omega\). A subset of \(\Omega\) is a base for \(G\) if its pointwise stabilizer in \(G\) is trivial. The minimal size of a base for \(G\) is denoted by \(b(G)\). In the present paper, the authors determine the precise value of \(b(G)\) for every primitive almost simple sporadic group \(G\), with the ...
Burness, Timothy C. +2 more
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Cherlin’s conjecture for sporadic simple groups [PDF]
Pacific Journal of Mathematics, 2018 11 pages; to appear in Pacific Journal of ...
Dalla Volta, Francesca +2 more
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