For every finite quasisimple group of Lie type G, every irreducible character χ of G, and every
element g of G, we give an exponential upper bound for the character ratio |χ(g)|/χ(1) with …

After a forty-year lull, the study of word-values in groups has sprung back into life with some
spectacular new results in finite group theory. These are largely motivated by applications to …

Let $ p $ be a polynomial in several non-commuting variables with coefficients in a field $ K
$ of arbitrary characteristic. It has been conjectured that for any $ n $, for $ p $ multilinear …

The classical Waring 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 non …

Equations over groups Page 1 Groups Complex. Cryptol. 4 (2012), 191 – 239 DOI 10.1515/gcc-2012-0015
© de Gruyter 2012 Equations over groups Vitaliı Roman’kov Abstract. This paper is a survey …

This paper contains a survey of recent developments in the investigation of word equations
in simple matrix groups and polynomial equations in simple (associative and Lie) matrix …

Let $ p $ be a multilinear polynomial in several non-commuting variables with coefficients in
a quadratically closed field $ K $ of any characteristic. It has been conjectured that for any …

We first note that a result of Gowers on product-free sets in groups has an unexpected
consequence: If k is the minimal degree of a representation of the finite group G, then for …

We establish new characterizations of primitive elements and free factors in free groups,
which are based on the distributions they induce on finite groups. For every finite group $ G …

In this survey paper we show how character methods can be used to solve a wide range of
seemingly unrelated problems. These include commutators, powers of conjugacy classes …