Bounded conciseness in the space of marked groups

TL;DR

This paper demonstrates that bounded conciseness is a closed property within the space of marked groups and reformulates a related conjecture about conciseness in residually finite groups.

Contribution

It establishes the closedness of bounded conciseness in the space of marked groups and reformulates a conjecture concerning conciseness in residually finite groups.

Findings

Bounded conciseness is a closed property in the space of marked groups.

Reformulation of a conjecture on conciseness in residually finite groups.

Provides a new perspective on the structure of marked groups.

Abstract

We prove that bounded conciseness is a closed property in the space of marked groups. As a consequence, we reformulate a conjecture of Fern\'andez-Alcober and Shumyatsky [7] about conciseness in the class of residually finite groups.