Finitely generated infinite simple groups of infinite square width and vanishing stable commutator length

TL;DR

This paper constructs finitely generated infinite simple groups with infinite width properties where stable commutator length vanishes, and provides a recursive presentation with decidable word and conjugacy problems.

Contribution

It introduces new finitely generated infinite simple groups exhibiting infinite width and vanishing stable commutator length, with a recursive presentation and decidable problems.

Findings

Existence of finitely generated infinite simple groups with infinite commutator and square width.

Stable commutator length vanishes on these groups.

A recursive presentation with decidable word and conjugacy problems.

Abstract

It is shown that there exist finitely generated infinite simple groups of infinite commutator width and infinite square width on which there exists no stably unbounded conjugation-invariant norm, and in particular stable commutator length vanishes. Moreover, a recursive presentation of such a group with decidable word and conjugacy problems is constructed.