43 citations · 124 across the 25 of their papers we have counts for
4 papers · 1 filter
On the diameters of McKay graphs for finite simple groups
Martin W. Liebeck, Aner Shalev, Pham Huu Tiep
Let be a finite group, and a nontrivial character of . The McKay graph has the irreducible characters of as vertices, with an edge from to…
Almost PI algebras are PI
Michael Larsen, Aner Shalev
We define the notion of an almost polynomial identity of an associative algebra , and show that its existence implies the existence of an actual polynomial identity of . A si…
Words, permutations, and the nonsolvable length of a finite group
Alexander Bors, Aner Shalev
We study the impact of certain identities and probabilistic identities on the structure of finite groups. More specifically, let be a nontrivial word in distinct variables…
Girth, words and diameter
Martin W. Liebeck, Aner Shalev
We study the girth of Cayley graphs of finite classical groups G on random sets of generators. Our main tool is an essentially best possible bound we obtain on the probability that…