43 citations · 124 across the 25 of their papers we have counts for
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math.GR2007★ 43 cited
Commutator maps, measure preservation, and T-systems
Shelly Garion, Aner Shalev
Let G be a finite simple group. We show that the commutator map is almost equidistributed as the order of G goes to infinity. This somewhat surprising result…
math.PR2007★ 31 cited
On the girth of random Cayley graphs
Alex Gamburd, Shlomo Hoory, Mehrdad Shahshahani +2
We prove that random d-regular Cayley graphs of the symmetric group asymptotically almost surely have girth at least (log_{d-1}|G|)^{1/2}/2 and that random d-regular Cayley graphs…
math.GR2007★ 1 cited
Word maps and Waring type problems
Michael Larsen, Aner Shalev
Waring's classical problem deals with expressing every natural number as a sum of g(k) k-th powers. Recently there has been considerable interest in similar questions for nonabelia…