Diameters of finite simple groups: sharp bounds and applications

177 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Derangements in simple and primitive groups (2002, methodology): “We mention that upper bounds on numbers of conjugacy classes are also of interest in random walks [Gl], [ LiSh ] and for computation of Fourier transforms on finite groups [MR].”
Word maps, conjugacy classes, and a noncommutative Waring-type theorem (2009, background): “12 of [19] that there exists an absolute constant c, such that if G is a finite simple group, and x 2G is chosen at random, then we have .”
Commutator maps, measure preservation, and T-systems (2007, background): “Word maps on algebraic groups and on ﬁnite simple groups have been the subject of active investigations in recent years; see [Bo], [LiSh2], [La], [Sh] and [LaSh].”
Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks (2004, unknown): “See also [18, 29] for some results on random walks on groups of Lie type.”
FINITARY APPROXIMATIONS OF GROUPS AND THEIR APPLICATIONS (2017, methodology): “The proof makes use of seminal results of Liebeck and Shalev [2001] and Nikolov and Segal [2012].”