The dynamical approach to the conjugacy in groups

摘要

Given a discrete group G, we identify the Stone-aech compactification beta G with the set of all ultrafilters on G and put G* = beta G G. The action G on G by the conjugations (g, x) bar right arrow g(-1) xg induces the action of G on G* by (g, p) bar right arrosw p(g), p(g) = {g(-1) : P is an element of p}. We study interplays between the algebraic properties of G and the dynamical properties of (G, G*). In particular, we show that p(G) is finite for each p is an element of G* if and only if the commutant of G is finite. (C) 2021 Elsevier B.V. All rights reserved.