These notes concern aspects of various graphs whose vertex set is a group $ G $ and
whose edges reflect group structure in some way (so that they are invariant under the action …

The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramified
Brauer group of a given quotient space. We derive a homological version of the Bogomolov …

We give the first examples of finite groups G such that the Chow ring of the classifying space
BG depends on the base field, even for fields containing the algebraic closure of ℚ. As a …

Let k be any field, G be a finite group acting on the rational function field k(x_g:g∈G) by
h⋅x_g=x_hg for any h,g∈G. Define k(G)=k(x_g:g∈G)^G. Noether's problem asks whether …

We describe the group| $ Aut_ {br}^ 1 ({\cal Z}(G)) $| A utbr 1 (Z (G)) of braided tensor
autoequivalences of the Drinfeld centre of a finite group G isomorphic to the identity functor …

We give the complete stably rational classification of algebraic tori of dimensions $4 $ and
$5 $ over a field $ k $. In particular, the stably rational classification of norm one tori whose …

The purpose of this note is to define a graph whose vertex set is a finite group GG, whose
edge set is contained in that of the commuting graph of GG and contains the enhanced …

Let K be any field and G be a finite group acting on the rational function field K (xg: g∈ G) by
h⋅ xg= x hg for any g, h∈ G. Define K (G)= K (xg: g∈ G) G. Noether's problem asks whether …

Let K be any field, G be a finite group. Let G act on the rational function field K (xg: g∈ G) by
K-automorphisms defined by h⋅ xg= xhg for any g, h∈ G. Denote by [Formula: see text] the …

We give a brief survey of recent results on word maps on simple groups and polynomial
maps on simple associative and Lie algebras. Our focus is on parallelism between these …