A one-relator group with long lower central series

TL;DR

This paper constructs a specific one-relator group with a lower central series of length ^2, providing a solution to an open problem posed by G. Baumslag.

Contribution

It introduces a novel example of a one-relator group with an exceptionally long lower central series, advancing understanding of group series complexity.

Findings

Constructed a one-relator group with lower central series of length ^2

Answered Baumslag's open problem about the possible length of such series

Demonstrated the existence of groups with highly complex lower central series

Abstract

A one-relator group with lower central series of length \omega^2 is constructed. This answers a problem of G. Baumslag.