Local indicability of groups with homology circle presentations

TL;DR

This paper explores conditions ensuring local indicability in groups with homology circle presentations, extending known results to broader classes like LOT groups and certain Adian presentations.

Contribution

It generalizes Howie's result for two-relator presentations to groups with homology circle presentations, applying this to LOT groups and non-cycle-free Adian presentations.

Findings

Established new conditions for local indicability in these groups.

Extended previous results to broader classes of groups.

Provided applications to LOT groups and specific Adian presentations.

Abstract

We investigate conditions that guarantee local indicability of groups that admit presentations with the homology of a circle, generalizing a result of J. Howie for two-relator presentations. We apply our results to investigate local indicability of LOT groups and some classes of non-cycle-free Adian presentations, extending previous results in that direction by J. Howie and D. Wise.