43 citations · 124 across the 25 of their papers we have counts for
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math.GR2019
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…
math.GR2019
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…
math.GR2019
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…