Krull-Schmidt Theorem for small profinite groups
Group Theory
2024-12-11 v1
Abstract
We prove that every small profinite group can be decomposed into a direct product of indecomposable profinite groups, and that such a decomposition is unique up to order and isomorphisms of the components. We also investigate the cancellation property of some free pro- groups, and give a new criterion for a profinite group to be small.
Keywords
Cite
@article{arxiv.2412.07699,
title = {Krull-Schmidt Theorem for small profinite groups},
author = {Tamar Bar-On and Nikolay Nikolov},
journal= {arXiv preprint arXiv:2412.07699},
year = {2024}
}