We prove some results in group theory in a model theoretic spirit.(i) We construct Jonsson
groups of cardinality 84, and other cardinalities as well. This answers an old question of …

This is a survey on the recent progress in minimal topological groups, with a particular
emphasis on constructions leading to non-abelian minimal groups, as semidirect products …

According to Markov (1946)[24], a subset of an abelian group G of the form {x∈ G: nx= a}, for
some integer n and some element a∈ G, is an elementary algebraic set; finite unions of …

In this paper, we establish a connection between categorical closedness and
nontopologizability of semigroups. In particular, for the class 𝖳 𝟣⁢ 𝖲 of T 1 topological …

These notes provide a brief introduction to topological groups with a special emphasis on
Pontryagin-van Kampen's duality theorem for locally compact abelian groups. We give a …

Some applications of graded diagrams in combinatorial group theory Page 24 SOME
APPLICATIONS OF GRADED DIAGRAMS IN COMBINATORIAL GROUP THEORY SERGEI V …

Every proper closed subgroup of a connected Hausdorff group must have index at least c,
the cardinality of the continuum. 70 years ago Markov conjectured that a group G can be …

Publisher Summary This chapter discusses selected topics from the structure theory of
topological groups. It contains open problems and questions covering the a number of topics …

Let c denote the cardinality of the continuum. Using forcing we produce a model of ZFC+ CH
with 2c “arbitrarily large” and, in this model, obtain a characterization of the Abelian groups …

Two non-discrete T1 topologies τ1, τ2 on a set X are called independent if their intersection
τ1∩ τ2 is the cofinite topology on X. We show that a countable group does not admit a pair …