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Generation by Conjugate Elements of Finite Almost Simple Groups With a Sporadic Socle [PDF]

Известия Иркутского государственного университета: Серия "Математика"
We study the minimum number of elements in the conjugacy class of an automorphism of a sporadic simple group that generate a subgroup containing all inner automorphisms.
D. O. Revin, A. V. Zavarnitsine
doaj   +2 more sources

Integral group ring of the Suzuki sporadic simple group [PDF]

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.
V. Bovdi, A. Konovalov, E. Marcos
semanticscholar   +4 more sources

ON THE CHARACTERISATION OF SPORADIC SIMPLE GROUPS BY CODEGREES

Bulletin of the Australian Mathematical Society, 2023
Let G be a finite group and $\mathrm {Irr}(G)$ the set of all irreducible complex characters of G. Define the codegree of $\chi \in \mathrm {Irr}(G)$ as $\mathrm {cod}(\chi ):={|G:\mathrm {ker}(\chi ) |}/{\chi (1)}$ and denote by $\mathrm {cod}(G):
Mallory Dolorfino, Luke Martin, Zachary Slonim, Yuxuan Sun, Yongqiang Yang   +4 more
semanticscholar   +4 more sources

Exotic Fusion Systems Related to Sporadic Simple Groups

Mathematical Proceedings of the Cambridge Philosophical Society, 2022
We describe several exotic fusion systems related to the sporadic simple groups at odd primes. More generally, we classify saturated fusion systems supported on Sylow 3-subgroups of the Conway group $\textrm{Co}_1$ and the Thompson group $\textrm{F}_3$
M. van Beek
semanticscholar   +3 more sources

Two Short Presentations for Lyons' Sporadic Simple Group [PDF]

Experimental Mathematics, 2000
Using an algorithm developed by the author, two new presentations for R. Lyons' sporadic simple group Ly are established, which contain fewer relations and are shorter than previously known ones.
Volker Gebhardt
semanticscholar   +4 more sources

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
openaire   +3 more sources

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., Müller, Jürgen, O'Brien, E.A., Wilson, Robert A.   +3 more
openaire   +7 more sources

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.
openaire   +3 more sources

Greedy base sizes for sporadic simple groups

Journal of Group Theory
A base for a permutation group 𝐺 acting on a set Ω is a sequence ℬ of points of Ω such that the pointwise stabiliser G B G_{\mathcal{B}} is trivial. Denote the minimum size of a base for 𝐺 by b ⁢ ( G ) b(G) .
Coen del Valle
semanticscholar   +4 more sources

Sporadic simple groups as flag‐transitive automorphism groups of symmetric designs [PDF]

Journal of combinatorial designs (Print), 2023
In this article, we study symmetric designs admitting flag‐transitive, point‐imprimitive almost simple automorphism groups with socle sporadic simple groups.
S. H. Alavi, A. Daneshkhah
semanticscholar   +1 more source