Set-Theoretical Problems in Asymptology

Банах, Тарас; Протасов, Ігор

doi:10.48550/arxiv.2004.01979

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2020

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“…In the case X = G and gx is the product of g and x in G, (G, G * ) is studied in [2]. The general case of (G, X * ) aroused in Asymptology, see the survey [4] and [1,Section 5].…”

Section: Introductionmentioning

confidence: 99%

The dynamical approach to the conjugacy in groups

Протасов¹,

Protasova²

2020

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Given a discrete group G, we identify the Stone-Čech compactification βG with the set of all ultrafilters on G and put G * = βG \ G. The action G on G by the conjugations (g, x) → g −1 xg induces the action of G on G * by (g, p) → p g , p g = {g −1 P g : P ∈ 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 ∈ G * if and only if the commutant of G is finite.1991 MSC: 20E45, 54D80.Keywords: space G * of ultrafilters on a group G, the action of G on G * by the conjugations, ultracenter of G * .

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“…In the case X = G and gx is the product of g and x in G, (G, G * ) is studied in [2]. The general case of (G, X * ) aroused in Asymptology, see the survey [4] and [1,Section 5].…”

Section: Introductionmentioning

confidence: 99%