A. Shalev

activity

20042022

most citedCommutator maps, measure preservation, and T-systems

43 citations · 124 across the 25 of their papers we have counts for

collaborators

Showing 2018Show all

6 papers · 1 filter

math.GR2018

Zero-one generation laws for finite simple groups

Robert M. Guralnick, Martin W. Liebeck, Frank Lübeck +1

Let $G$ be a simple algebraic group over the algebraic closure of $GF (p)$ ( $p$ prime), and let $G (q)$ denote a corresponding finite group of Lie type over $GF (q)$ , where $q$ is a p…

math.GR2018

Probabilistic Waring problems for finite simple groups

Michael Larsen, Aner Shalev, Pham Huu Tiep

The probabilistic Waring problem for finite simple groups asks whether every word of the form $w_{1} w_{2}$ , where $w_{1}$ and $w_{2}$ are non-trivial words in disjoint sets of variables, i…

math.GR2018

Character ratios, representation varieties and random generation of finite groups of Lie type

Martin W. Liebeck, Aner Shalev, Pham H. Tiep

We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie…

math.GR2018

The length and depth of compact Lie groups

Timothy C. Burness, Martin W. Liebeck, Aner Shalev

Let $G$ be a connected Lie group. An unrefinable chain of $G$ is a chain of subgroups $G = G_{0} > G_{1} > \dots > G_{t} = 1$ , where each $G_{i}$ is a maximal connected subgroup of $G_{i-…

math.GR2018★ 9 cited

On the length and depth of finite groups (with an appendix by D.R. Heath-Brown)

Timothy C. Burness, Martin W. Liebeck, Aner Shalev

An unrefinable chain of a finite group $G$ is a chain of subgroups $G = G_{0} > G_{1} > \dots > G_{t} = 1$ , where each $G_{i}$ is a maximal subgroup of $G_{i - 1}$ . The length (respectively…

math.GR2018

Probabilistically nilpotent groups

Aner Shalev

We show that, for a finitely generated residually finite group $Γ$ , the word $[x_{1}, \dots, x_{k}]$ is a probabilistic identity of $Γ$ if and only if $Γ$ is virtually nilpotent of cl…