Zobrazeno 1 - 10
of 536
pro vyhledávání: '"20D06"'
Autor:
Korhonen, Mikko
Let $G$ be the finite simple group of Lie type $G = E_7(q)$, where $q$ is an odd prime power. Then $G$ is an index $2$ subgroup of the adjoint group $G_{\operatorname{ad}}$, which is also denoted by $G_{\operatorname{ad}} = \operatorname{Inndiag}(G)$
Externí odkaz:
http://arxiv.org/abs/2409.20281
Autor:
Grechkoseeva, M. A., Vasil'ev, A. V.
The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups with abelian Sylow $2$-subgroups. For every positive integer $k$, we fin
Externí odkaz:
http://arxiv.org/abs/2409.15873
Autor:
Dona, Daniele
The Liebeck-Nikolov-Shalev conjecture [LNS12] asserts that, for any finite simple non-abelian group $G$ and any set $A\subseteq G$ with $|A|\geq 2$, $G$ is the product of at most $N\frac{\log|G|}{\log|A|}$ conjugates of $A$, for some absolute constan
Externí odkaz:
http://arxiv.org/abs/2409.11246
Autor:
Baykalov, Anton A.
Let $G$ be a transitive permutation group on a finite set with solvable point stabiliser. In 2010, Vdovin conjectured that the base size of $G$ is at most 5. Burness proved this conjecture in the case of primitive $G$. The problem was reduced by Vdov
Externí odkaz:
http://arxiv.org/abs/2408.08510
Liebeck, Nikolov, and Shalev conjectured that for every subset A of a finite simple group S with |A|>1, there exist O( log|S| / log|A| ) conjugates of A whose product is S. This paper is a companion to [Lifshitz: Completing the proof of the Liebeck-N
Externí odkaz:
http://arxiv.org/abs/2408.07800
Autor:
Kundu, Rijubrata, S, Velmurugan
The covering number of a non-linear character $\chi$ of a finite group $G$ is the least positive integer $k$ such that every irreducible character of $G$ occurs in $\chi^k$. We determine the covering numbers of irreducible characters of the symmetric
Externí odkaz:
http://arxiv.org/abs/2407.04054
Autor:
Skresanov, Saveliy V.
We show that some classical results on expander graphs imply growth results on normal subsets in finite simple groups. As one application, it is shown that given a nontrivial normal subset $ A $ of a finite simple group $ G $ of Lie type of bounded r
Externí odkaz:
http://arxiv.org/abs/2406.12506
Autor:
Liebeck, Martin W., Praeger, Cheryl E.
We determine all factorisations $X=AB$, where $X$ is a finite almost simple group and $A,B$ are core-free subgroups such that $A\cap B$ is cyclic or dihedral. As a main application, we classify the graphs $\Gamma$ admitting an almost simple arc-trans
Externí odkaz:
http://arxiv.org/abs/2405.14287
Autor:
Fumagalli, Francesco, Maróti, Attila
If $A$, $B$, $C$ are subsets in a finite simple group of Lie type $G$ at least two of which are normal with $|A||B||C|$ relatively large, then we establish a stronger conclusion than $ABC = G$. This is related to a theorem of Gowers and is a generali
Externí odkaz:
http://arxiv.org/abs/2404.04967
Autor:
Panja, Saikat
Let $G$ be one of the finite general linear, unitary, symplectic or orthogonal groups over finite fields of odd order. We find the cardinality of the fibers of the square map at a given generic element. Using this we find the number of real conjugacy
Externí odkaz:
http://arxiv.org/abs/2403.17096