Zobrazeno 1 - 10
of 833
pro vyhledávání: '"20G40"'
Autor:
Panja, Saikat, Singh, Anupam
The study of word maps on groups has been of deep interest in recent years. This survey focuses on the case of power maps on groups; $viz.$ the map $x\mapsto x^M$ for a group $G$, and an integer $M\geq 2$. Here, we accumulate various results on the s
Externí odkaz:
http://arxiv.org/abs/2411.07017
Autor:
Jones, Gareth A.
We obtain formulae for the numbers of isomorphism and conjugacy classes of non-identity proper subgroups of the groups $G={\rm PSL}_2(p)$, $p$ prime, and for the numbers of those conjugacy classes which do or do not consist of self-normalising subgro
Externí odkaz:
http://arxiv.org/abs/2411.02219
Autor:
Cabanes, Marc, Späth, Britta
McKay's conjecture (1971) on character degrees was reduced by Isaacs-Malle-Navarro (2007) to a so-called inductive condition on characters of finite quasisimple groups [IMN07], thus opening the way to a proof of McKay's conjecture using the classific
Externí odkaz:
http://arxiv.org/abs/2410.20392
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:
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:
Zamboni, Luca Q.
By a Christoffel matrix we mean a $n\times n$ matrix corresponding to the lexicographic array of a Christoffel word of length $n.$ If $R$ is an integral domain, then the product of two Christoffel matrices over $R$ is commutative and is a Christoffel
Externí odkaz:
http://arxiv.org/abs/2409.07974
Autor:
Garzoni, Daniele
We prove that if $G$ is a transitive permutation group of sufficiently large degree $n$, then either $G$ is primitive and Frobenius, or the proportion of derangements in $G$ is larger than $1/(2n^{1/2})$. This is sharp, generalizes substantially boun
Externí odkaz:
http://arxiv.org/abs/2409.03305
Autor:
Lübeck, Frank, Shoji, Toshiaki
In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group $G$. Generalized Green functions of $G$ can be computed by using Lusztig's algorithm, if split elements exist for any unipotent class. The ex
Externí odkaz:
http://arxiv.org/abs/2408.16960
Autor:
Rossi, Damiano
Webb's conjecture states that the orbit space of the Brown complex of a finite group at any given prime $\ell$ is contractible. This conjecture was proved by Symonds in 1998. In this paper, we suggest a generalisation of Webb's conjecture for finite
Externí odkaz:
http://arxiv.org/abs/2408.06129
In this article we prove orthogonality relations for deep level Deligne--Lusztig varieties of Coxeter type, attached to a reductive group over a local non-archimedean field, which splits over an unramified extension. This extends results of Dudas and
Externí odkaz:
http://arxiv.org/abs/2407.18694