On pro-p Cappitt groups with finite exponent
Group Theory
2023-09-06 v1
Abstract
A pro-p Cappitt group is a pro-p group G such that the subgroup topologically generated by all non-normal closed subgroups is a proper subgroup of G. In this paper we prove that non-abelian pro-p Cappitt groups whose torsion subgroup is closed has finite exponent. We also prove that in a pro-p Cappitt group its subgroup commutator is a procyclic central subgroup. Finally we show that pro-2 Cappitt groups of exponent 4 are pro-2 Dedekind groups. These results are pro-p versions of the generalized Dedekind groups studied by Cappitt.
Keywords
Cite
@article{arxiv.2309.00914,
title = {On pro-p Cappitt groups with finite exponent},
author = {Anderson Porto and Igor Lima},
journal= {arXiv preprint arXiv:2309.00914},
year = {2023}
}