Results 1 to 10 of about 32 (30)
The Maximal Size of a Minimal Generating Set
Forum of Mathematics, Sigma, 2023 A generating set for a finite group G is minimal if no proper subset generates G, and $m(G)$ denotes the maximal size of a minimal generating set for G. We prove a conjecture of Lucchini, Moscatiello and Spiga by showing that there exist $a,b>
Scott Harper
exaly +3 more sources
Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 657-673, August 2020., 2020 Abstract Every finite simple group can be generated by two elements, and Guralnick and Kantor proved that, moreover, every nontrivial element is contained in a generating pair. Groups with this property are said to be 32‐generated. Thompson's group V was the first finitely presented infinite simple group to be discovered.
Casey Donoven, Scott Harper
wiley +1 more source
LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS
Forum of Mathematics, Sigma, 2017 We use the structure lattice, introduced in Part I, to undertake a systematic study of the class $\mathscr{S}$ consisting of compactly generated ...
PIERRE-EMMANUEL CAPRACE +2 more
doaj +1 more source
$A_{1}$-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS
Forum of Mathematics, Sigma, 2019 Let $G$ be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic $p>0$ and let $X=\text{PSL}_{2}(p)$ be a subgroup of $G$ containing a regular unipotent element $x$ of $G$. By a theorem of Testerman, $x$
TIMOTHY C. BURNESS, DONNA M. TESTERMAN
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On derangements in simple permutation groups
Forum of Mathematics, SigmaLet $G \leqslant \mathrm {Sym}(\Omega )$ be a finite transitive permutation group and recall that an element in G is a derangement if it has no fixed points on $\Omega $ . Let $\Delta (G)$ be the set of derangements in G and define
Timothy Burness, Marco Fusari
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On the depth of subgroups of simple groups
Forum of Mathematics, SigmaThe depth of a subgroup H of a finite group G is a positive integer defined with respect to the inclusion of the corresponding complex group algebras $\mathbb {C}H \subseteq \mathbb {C}G$ .
Timothy C. Burness
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Strongly Base-Two Groups. [PDF]
Vietnam J Math, 2023 Burness TC, Guralnick RM.
europepmc +1 more source
Embeddings into left-orderable simple groups. [PDF]
J Lond Math Soc, 2022 Darbinyan A, Steenbock M.
europepmc +1 more source
Representations of extensions of simple groups. [PDF]
Arch MathHarper S, Liebeck MW.
europepmc +1 more source