Products of finite groups and nonmeasurable subgroups

TL;DR

The paper proves that for any finite group G, the infinite product G^ω contains 2^c dense nonmeasurable subgroups, and provides additional examples of such subgroups in compact groups.

Contribution

It introduces new examples of dense nonmeasurable subgroups in compact groups, expanding understanding of measure theory in group products.

Findings

G^ω has 2^c dense nonmeasurable subgroups for finite G

Additional examples of compact groups with dense nonmeasurable subgroups

Advances the study of measure and subgroup structure in topological groups

Abstract

It is proven that if $G$ is a finite group, then $G^\omega$ has $2^{\mathfrak c}$ dense nonmeasurable subgroups. Also, other examples of compact groups with dense nonmeasurable subgroups are presented.