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 …

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 noncommuting variables, with coefficients in
an algebraically closed field $ K $ of arbitrary characteristic. In this paper we classify the …

Let D be a division algebra of degree m. The first aim of this paper is to show that if D is tame
and totally ramifield and if the center of D is Henselian, then there exists a positive d …

We consider word maps and word maps with constants on a simple algebraic group G. We
present results on the images of such maps, in particular, we prove a theorem on the …

We present a survey of results on word equations in simple groups, as well as their
analogues and generalizations, which were obtained over the past decade using various …

Kaplansky asked about the possible images of a polynomial f in several noncommuting
variables. In this paper, we consider the case of fa Lie polynomial. We describe all the …

We extend Borel's theorem on the dominance of word maps from semisimple algebraic
groups to some perfect groups. In another direction, we generalize Borel's theorem to some …

Let n\geqslant 2 n⩾ 2 be an integer and F_n F n the free group on n generators, its first and
second derived subgroups. Let K be an algebraically closed field of characteristic zero. We …

For $ n\geq 2$, we consider the map on $ M_n (\mathbb K) $ given by evaluation of a
polynomial $ f (X_1,\ldots, X_m) $ over the field $\mathbb K $. In this article, we explore the …