Regular semitopological groups of every countable sequential order

Remarks on extremally disconnected semitopological groups

Answering recent question of A.V. Arhangel’skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.

PI11-CA0 and Order Types of Countable Ordered Groups

Groups with regular automorphisms of order four

An automorphism of a group G is called regular if it moves every element of G except the identity. BURNSIDE proved that a finite group G has a regular automorphism of order two if and only if G is an abelian group of odd order, and then the only such automorphism maps every element onto its inverse ([21, p. 230). More recently several authors considered the question: what groups can admit regul...

Countable Primitive Groups

We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a special case Kleinian groups as well as subgroups of word hyperbolic groups. As an application we calculate the Frattini subgroup in many of these settings, oft...

Automorphism groups of countable structures

Suppose M is a countable first-order structure with a ‘rich’ automorphism group Aut(M). We will study Aut(M) both as a group and as a topological group, where the topology is that of pointwise convergence. This involves a mixture of model theory, group theory, combinatorics, descriptive set theory and topological dynamics. Here, ‘rich’ is undefined and depends on the context, but examples which...