Аннотация:
Let Fm be the free group of rank m. Then for any word w=w(x1,…,xm)∈Fm and for any group G one can define the word map˜w:Gm→G
by the formula: ˜w((g1,…,gm)):=w(g1,…,gm).
Word maps have been intensely studied over at least two past decades
in various contexts. In this talk we deal with the case where
G=G(K) is the group of K-points of a simple linear
algebraic group G defined over a
field K. Here we consider the problem of surjectivity of word maps and also some related
questions.