33 Citations
Groups with cofinite Zariski topology and potential density
- Mathematics
- 2021
Tkachenko and Yaschenko [34] characterized the abelian groups G such that all proper unconditionally closed subsets of G are finite, these are precisely the abelian groups G having cofinite Zariski…
Productivity of the Zariski topology on groups
- Mathematics
- 2013
This paper investigates the productivity of the Zariski topology ZG of a group G. If G = {Gi | i 2 I} is a family of groups, and G = Q i2I Gi is their direct product, we prove that ZGQ i2I ZGi. This…
Topological groups described by their continuous homomorphisms or small subgroups
- Mathematics
- 2020
Continuing the classical work of Bohr on almost periodic functions, in 1940 von Neumann introduced the concept of a minimally almost periodic (MinAP) group. A topological group is MinAP if all its…
Characterized Subgroups of Topological Abelian Groups
- MathematicsAxioms
- 2015
This work introduces the relevant class of autochacaracterized groups (namely, the groups that are characterized subgroups of themselves by means of a sequence of non-null characters); in the case of locally compact abelian groups, these are proved to be exactly the non-compact ones.
MARKOV'S PROBLEMS THROUGH THE LOOKING GLASS OF ZARISKI AND MARKOV TOPOLOGIES
- Mathematics
- 2011
Markov posed a series of challenging problems on infinite groups. We discuss a unified approach to four of them, based on the extensive use of several topologies that allows for their better…
Verbal functions of a group
- Mathematics
- 2014
The aim of this paper is the study of elementary algebraic subsets of a group G, rst dened by Markov in 1944 as the solution- set of a one-variable equation over G. We introduce the group of words…
References
SHOWING 1-10 OF 36 REFERENCES
ALGEBRAIC STRUCTURE OF SMALL COUNTABLY COMPACT ABELIAN GROUPS
- Mathematics
- 2003
Under Martin’s Axiom, we completely characterize the algebraic structure of Abelian groups of the size c that admit a countably compact Hausdor group topology. It turns out that, in the torsion case,…
Reflection principle characterizing groups in which unconditionally closed sets are algebraic
- Mathematics
- 2007
Abstract We give a necessary and sufficient condition, in terms of a certain reflection principle, for every unconditionally closed subset of a group G to be algebraic. As a corollary, we prove that…
Topological Groups and Semigroups
- Mathematics
- 1988
1°. A topological group is a group endowed with a Hausdorff topology relative to which the operations of multiplication and inversion are continuous (the latter being therefore a homeomorphism); here…