On periodic groups having almost regular 2-elements

Characterization of almost maximally almost-periodic groups

Let G be an abelian group. We prove that a group G admits a Hausdorff group topology τ such that the von Neumann radical n(G, τ) of (G, τ) is non-trivial and finite iff G has a non-trivial finite subgroup. If G is a topological group, then n(n(G)) 6= n(G) if and only if n(G) is not dually embedded. In particular, n(n(Z, τ)) = n(Z, τ) for any Hausdorff group topology τ on Z. We shall write our a...

Almost Periodic Transformation Groups* By

1. In view of the recent work on topological groups it is natural to consider the situation which arises when such groups act as transformation groups on various types of spaces. Such a study is begun here from the point of view of almost periodic transformation groups, the definition of which is suggested by von Neumann's paper on almost periodic functions in a group.f Compact topological tran...

Notes on Periodic Elements of Garside Groups

Let G be a Garside group with Garside element ∆. An element g ∈ G is said to be periodic with respect to ∆ if some power of g lies in the cyclic group generated by ∆. This paper shows the following. (i) The periodicity of an element does not depend on the choice of a particular Garside structure if and only if the center of G is cyclic. (ii) If g = ∆ for some nonzero integer k, then g is conjug...

Almost commuting elements in compact Lie groups

2 00 8 Which infinite abelian torsion groups admit an almost maximally almost - periodic group topology ? *

A topological group G is said to be almost maximally almost-periodic if its von Neumann radical n(G) is non-trivial, but finite. In this paper, we prove that (a) every countably infinite abelian torsion group, (b) every abelian torsion group of cardinality greater than continuum, and (c) every (non-trivial) divisible abelian torsion group admits a (Hausdorff) almost maximally almost-periodic gr...