Cyclic Subgroups of Belk-Hyde-Matucci Group $V\!\mathcal{A}$

TL;DR

This paper proves that the Belk-Hyde-Matucci group $V\mathcal{A}$, which contains all countable abelian groups, does not have subgroups with distorted cyclic subgroups.

Contribution

It establishes a new property of the Belk-Hyde-Matucci group regarding the absence of distorted cyclic subgroups.

Findings

$V\mathcal{A}$ contains no distorted cyclic subgroups.

$V\mathcal{A}$ includes all countable abelian groups.

The group has specific subgroup distortion properties.

Abstract

In this paper it is proved that the Belk-Hyde-Matucci group $V\!\mathcal{A}$, a group containing every countable abelian group, does not contain subgroups with distorted cyclic subgroups.