43 citations · 124 across the 25 of their papers we have counts for
4 papers · 2 filters
The length and depth of algebraic groups
Timothy C. Burness, Martin W. Liebeck, Aner Shalev
Let be a connected algebraic group. An unrefinable chain of is a chain of subgroups , where each is a maximal connected subgroup of…
The depth of a finite simple group
Timothy C. Burness, Martin W. Liebeck, Aner Shalev
We introduce the notion of the depth of a finite group , defined as the minimal length of an unrefinable chain of subgroups from to the trivial subgroup. In this paper we in…
Character bounds for finite groups of Lie type
Roman Bezrukavnikov, Martin W. Liebeck, Aner Shalev +1
We establish new bounds on character values and character ratios for finite groups of Lie type, which are considerably stronger than previously known bounds, and which are best…
Words, Hausdorff dimension and randomly free groups
Michael Larsen, Aner Shalev
We study fibers of word maps in finite, profinite, and residually finite groups. Our main result is that, for any word w in the free group on d generators, there exists such…