Torsion subgroups of small cancellation groups
Abstract
We prove that torsion subgroups of groups defined by C(6), C(4)-T(4) or C(3)-T(6) small cancellation presentations are finite cyclic groups. This follows from a more general result on the existence of fixed points for locally elliptic (every element fixes a point) actions of groups on simply connected small cancellation complexes. We present an application concerning automatic continuity. We observe that simply connected C(3)-T(6) complexes may be equipped with a CAT(0) metric. This allows us to get stronger results on locally elliptic actions in that case. It also implies that the Tits Alternative holds for groups acting on simply connected C(3)-T(6) small cancellation complexes with a bound on the order of cell stabilisers.
Cite
@article{arxiv.2112.01912,
title = {Torsion subgroups of small cancellation groups},
author = {Karol Duda},
journal= {arXiv preprint arXiv:2112.01912},
year = {2025}
}
Comments
Change of title, previously 'Torsion subgroups of C(4)-T(4) small cancellation groups'. Major modifications of the lemmas concerning C(4)-T(4) case. Extended results to C(6) and C(3)-T(6) cases