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

41 papers

math.GR2022

Identities with coefficients in simple compact Lie groups

Michael Larsen, Aner Shalev

We conjecture that if $G$ is a simple compact Lie group with trivial center, then every $d$ -variable non-constant word map with coefficients in $G$ defines a non-constant function…

math.RA2022

From braces to pre-Lie rings

Aner Shalev, Agata Smoktunowicz

Let $A$ be a brace of cardinality $p^{n}$ where $p > n + 1$ is prime, and let $ann (p^{2})$ be the set of elements of additive order at most $p^{2}$ in this brace. We construct a pre-L…

math.RT2021

Representations and tensor product growth

Michael Larsen, Aner Shalev, Pham Huu Tiep

The deep theory of approximate subgroups establishes 3-step product growth for subsets of finite simple groups $G$ of Lie type of bounded rank. In this paper we obtain 2-step growt…

math.GR2021

Characteristic Covering Numbers of Finite Simple Groups

Michael Larsen, Aner Shalev, Pham Huu Tiep

We show that, if $w_{1}, \dots, w_{6}$ are words which are not an identity of any (non-abelian) finite simple group, then $w_{1} (G) w_{2} (G) \dots w_{6} (G) = G$ for all (non-abelian) finit…

math.GR2020

Permutation groups with restricted stabilizers

Timothy C. Burness, Aner Shalev

Fix a positive integer $d$ and let $Γ_{d}$ be the class of finite groups without sections isomorphic to the alternating group $A_{d}$ . The groups in $Γ_{d}$ were studied by Babai, Camero…

math.RA2020★ 1 cited

Random generation of associative algebras

Damian Sercombe, Aner Shalev

There has been considerable interest in recent decades in questions of random generation of finite and profinite groups, and finite simple groups in particular. In this paper we st…