Results 21 to 30 of about 12,824,044 (290)

Remarks on Conjectures in Block Theory of Finite Groups

Axioms, 2023
In this paper, we focus on Brauer’s height zero conjecture, Robinson’s conjecture, and Olsson’s conjecture regarding the direct product of finite groups and give relative versions of these conjectures by restricting them to the algebraic concept of the ...
Manal H. Algreagri, Ahmad M. Alghamdi
doaj   +1 more source

Quantitative characterization of finite simple groups: a complement [PDF]

International Journal of Group Theory
In this paper, we summarize the research on the characterization of finite simple groups and the study of finite groups based on their ``set of element orders" and ``two orders" (the order of the group and the set of element orders). We also discuss some
Wujie Shi
doaj   +1 more source

Control of transfer and weak closure in fusion systems. [PDF]

, 2010
We show that $\K_\infty$ and $\K^\infty$ control transfer in every fusion system on a finite $p$-group when $p \geq 5$, and that they control weak closure of elements in every fusion system on a finite $p$-group when $p \geq 3$.
Diaz, Antonio, Glesser, Adam, Mazza, Nadia, Park, Sejong   +3 more
core   +5 more sources

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
doaj   +1 more source

The maximal subgroups of the classical groups in dimension 13, 14 and 15 [PDF]

, 2015
One might easily argue that the Classification of Finite Simple Groups is one of the most important theorems of group theory. Given that any finite group can be deconstructed into its simple composition factors, it is of great importance to have a ...
Schröder, Anna Katharina
core   +2 more sources

On a Sufficient Condition for the Existence of a Periodic Part in the Shunkov Group

Известия Иркутского государственного университета: Серия "Математика", 2017
The group $ G $ is saturated with groups from the set of groups if any a finite subgroup $ K $ of $ G $ is contained in a subgroup of $ G $, which is isomorphic to some group in $ \mathfrak{X} $.
A.A. Shlepkin
doaj   +1 more source

Base sizes for simple groups and a conjecture of Cameron [PDF]

, 2009
Let G be a permutation group on a finite set ?. A base for G is a subset B C_ ? whose pointwise stabilizer in G is trivial; we write b(G) for the smallest size of a base for G. In this paper we prove that b(G) ?
Burness, TC, Liebeck, MW, Shalev, A, Liebeck, Martin W., Burness, Timothy C., Shalev, Aner   +5 more
core   +1 more source

The exact spread of M23 is 8064 [PDF]

International Journal of Group Theory, 2012
Let $G$ be a finite group. We say that $G$ has emph{spread} r if for any set of distinct non-trivial elements of $G$ $X:={x_1,ldots, x_r}subset G^{#}$ there exists an element $yin G$ with the property that $langle x_i,yrangle=G$ for every $1leq ileq r ...
B. Fairbairn
doaj  

Zassenhaus conjecture for central extensions of S5 [PDF]

, 2008
We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S5 and for the general linear group GLð2; 5Þ. The first result, together with others from the literature,
Bódi, Viktor, Hertweck, M., Victor Bovdi, Martin Hertweck, Gildea, Joe   +4 more
core   +1 more source

Endo-permutation modules as sources of simple modules. [PDF]

, 2003
The source of a simple $kG$-module, for a finite $p$-solvable group $G$ and an algebraically closed field $k$ of prime characteristic $p$, is an endo-permutation module (see~\cite{Pu1} or~\cite{Th}). L.
Mazza, Nadia
core   +4 more sources