arXiv Open Access 2021

Torsion subgroups of small cancellation groups

Karol Duda

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.GR

Penulis (1)

Karol Duda

Format Sitasi

APA MLA BibTeX

Duda, K. (2021). Torsion subgroups of small cancellation groups. https://arxiv.org/abs/2112.01912

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓