We prove that in every finitely generated profinite group, every subgroup of finite index is
open; this implies that the topology on such groups is determined by the algebraic structure …

Markov chains on finite sets are used in a great variety of situations to approximate,
understand and sample from their limit distribution. A familiar example is provided by card …

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 w=w(x_1,...,x_d)≠1 be a nontrivial group word. We show that if G is a sufficiently large
finite simple group, then every element g ϵ G can be expressed as a product of three values …

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 …

Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry,
combinatorial group theory, and other contexts. We use character-theoretic and probabilistic …

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 …

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 …