# Small-large subgroups of locally compact Abelian Polish groups

## TL;DR

This paper provides a simplified proof for the existence of null but non-meager subgroups in Abelian Polish groups, addressing questions about subgroup properties in locally compact groups.

## Contribution

It offers a simpler proof for the special case of Abelian Polish groups regarding null and non-meager subgroups, building on prior results.

## Key findings

- Confirmed existence of null but non-meager subgroups in Abelian Polish groups
- Provided a simpler proof for the special case of Abelian Polish groups
- Addressed questions about subgroup properties in locally compact groups

## Abstract

In [arXiv:1605.02261] Ros\l{}anowski and Shelah asked whether every locally compact non-discrete group has a null but non-meager subgroup, and conversely whether it is consistent with $ZFC$ that in every locally compact group there are no meager but non-null subgroups. The answer is affirmative for both questions [arXiv:1605.02261], however, in this paper we provide a much simpler proof for the special case of Abelian Polish groups.