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 2015 · math.GRShow all

3 papers · 2 filters

math.GR2015

Rapid expansion in finite simple groups

Martin W. Liebeck, Gili Schul, Aner Shalev

We show that small normal subsets $A$ of finite simple groups expand very rapidly -- namely, $∣ A^{2} ∣ \geq ∣ A ∣^{2 - ε}$ , where $ε > 0$ is arbitrarily small.

math.GR2015★ 4 cited

A probabilistic Tits alternative and probabilistic identities

Michael Larsen, Aner Shalev

We introduce the notion of a probabilistic identity of a residually finite group. We prove that a finitely generated linear group satisfies a probabilistic identity if and only if…

math.GR2015★ 1 cited

Surjective word maps and Burnsides $p^{a} q^{b}$ theorem

Robert Guralnick, Martin Liebeck, Eamon O'Brien +2

We prove surjectivity of certain word maps on finite non-abelian simple groups. More precisely, we prove the following: if N is a product of two prime powers, then the word map sen…

Rapid expansion in finite simple groups

A probabilistic Tits alternative and probabilistic identities

Surjective word maps and Burnsides paqb theorem

Surjective word maps and Burnsides $p^{a} q^{b}$ theorem