Zobrazeno 1 - 10
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pro vyhledávání: '"Liebeck, Martin W."'
Autor:
Harper, Scott, Liebeck, Martin W.
Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group $G$ factors through a projective representation of $G$, except for some groups of Lie type in chara
Externí odkaz:
http://arxiv.org/abs/2405.17593
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
Publikováno v:
Comm. Algebra, 52(9):3750--3761, 2024
Let $G$ be a finite non-abelian simple group, $C$ a non-identity conjugacy class of $G$, and $\Gamma_C$ the Cayley graph of $G$ based on $C \cup C^{-1}$. Our main result shows that in any such graph, there is an involution at bounded distance from th
Externí odkaz:
http://arxiv.org/abs/2402.08497
Let $\mathcal{C}$ be a conjugacy class of involutions in a group $G$. We study the graph $\Gamma(\mathcal{C})$ whose vertices are elements of $\mathcal{C}$ with $g,h\in\mathcal{C}$ connected by an edge if and only if $gh\in\mathcal{C}$. For $t\in \ma
Externí odkaz:
http://arxiv.org/abs/2402.08357
Let $G$ be a classical group defined over a finite field. We consider the following fundamental problems concerning conjugacy in $G$: 1. List a representative for each conjugacy class of $G$. 2. Given $x \in G$, describe the centralizer of $x$ in $G$
Externí odkaz:
http://arxiv.org/abs/2401.07557
Publikováno v:
J. Algebra 607 (2022), 531-606
We continue our work (started in ``Multiplicity-free representations of algebraic groups", arXiv:2101.04476), on the program of classifying triples $(X,Y,V)$, where $X,Y$ are simple algebraic groups over an algebraically closed field of characteristi
Externí odkaz:
http://arxiv.org/abs/2307.13328
Autor:
Gill, Nick, Liebeck, Martin W.
Publikováno v:
Pacific J. Math. 322 (2023) 281-300
We prove that the maximum length of an irredundant base for a primitive action of a finite simple group of Lie type is bounded above by a function which is a polynomial in the rank of the group. We give examples to show that this type of upper bound
Externí odkaz:
http://arxiv.org/abs/2212.07853
Let p be a prime and G a subgroup of GL(d)(p). We define G to be p-exceptional if it has order divisible by p, but all its orbits on vectors have size coprime to p. We obtain a classification of p-exceptional linear groups. This has consequences for
Externí odkaz:
http://hdl.handle.net/10150/614975
http://arizona.openrepository.com/arizona/handle/10150/614975
http://arizona.openrepository.com/arizona/handle/10150/614975
A permutation group is {\it binary} if its orbits on $k$-tuples, for any integer $k\geq 2$, can be deduced from its orbits on $2$-tuples. Cherlin conjectured that a finite primitive binary permutation group $G$ must lie in one of three known families
Externí odkaz:
http://arxiv.org/abs/2106.05154