Results 1 to 10 of about 31,876 (219)
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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Local Fusion Graphs and Sporadic Simple Groups [PDF]
The Electronic Journal of Combinatorics, 2015 For a group $G$ with $G$-conjugacy class of involutions $X$, the local fusion graph $\mathcal{F}(G,X)$ has $X$ as its vertex set, with distinct vertices $x$ and $y$ joined by an edge if, and only if, the product $xy$ has odd order. Here we show that, with only three possible exceptions, for all pairs $(G,X)$ with $G$ a sporadic simple group or the ...
Ballantyne, John, Rowley, Peter
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Involutions in the Automorphism Groups of Small Sporadic Simple Groups [PDF]
Algebra, 2015 For each of fifteen of the sporadic finite simple groups we determine the suborbits of its automorphism group in its conjugation action upon its involutions. Representatives are obtained as words in standard generators.
Bates, Chris +2 more
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Semi-Presentations for the Sporadic Simple Groups [PDF]
Experimental Mathematics, 2005 A semi-presentation for a group G is a set of relations which characterises a set of generators of G up to automorphism. We discuss some techniques for finding semi-presentations and illustrate them by exhibiting semi-presentations on standard generators for the 26 sporadic simple groups and their automorphism groups.
Nickerson, S. J., Wilson, R. A.
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Sporadic simple groups and quotient singularities [PDF]
Izvestiya: Mathematics, 2013 We show that the only sporadic simple group such that some of its faithful representations or some faithful representations of its stem extensions give rise to exceptional (weakly-exceptional but not exceptional, respectively) quotient singularities is the Hall-Janko group (the Suzuki group, respectively).
Cheltsov, I. A., Shramov, C. A.
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Amalgams Which Involve Sporadic Simple Groups I
Journal of Algebra, 1997 [For terminology and notions see the preceding review Zbl 0885.20013 of part I.] Part II is devoted to the commuting case. Here \(b=1\) and there are nine possible pairs \((P_1,P_2)\), eight of these are realized in one of the groups \(Co_2\), \(Co_1\), \(Fi_{22}\), \(\Aut(Fi_{22})\), \(Fi_{23}\), \(Fi_{24}'\), \(Fi_{24}\) and \(J_4\).
Parker, Christopher, Rowley, Peter
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Integral group ring of the Suzuki sporadic simple group
Publicationes Mathematicae Debrecen, 2008 Using the Luthar--Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle's conjecture on prime graphs.
Bódi, Viktor +2 more
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Sporadic simple groups as flag‐transitive automorphism groups of symmetric designs
Journal of Combinatorial Designs, 2023 AbstractIn this article, we study symmetric designs admitting flag‐transitive, point‐imprimitive almost simple automorphism groups with socle sporadic simple groups. As a corollary, we present a classification of symmetric designs admitting flag‐transitive automorphism group whose socle is a sporadic simple group, and in conclusion, there are exactly ...
Alavi, Seyed Hassan, Daneshkhah, Ashraf
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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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