A new family of sofic one-relator groups

TL;DR

This paper introduces an infinite family of sofic one-relator groups that are neither residually solvable nor residually finite, expanding understanding of group properties beyond previous methods.

Contribution

It presents a novel construction of sofic one-relator groups that do not possess residual solvability or residual finiteness, using a different proof technique from prior work.

Findings

Established existence of non-residually solvable sofic groups

Demonstrated groups are not residually finite

Provided a new proof approach independent of Magnus' decompositions

Abstract

We provide an infinite family of sofic one-relator groups that are not residually solvable nor residually finite. The proof is essentially different from the one in [1], as it does not require just Magnus' decompositions.