When is the Sum of Two Closed Subgroups Closed in a Locally Compact Abelian Group
Group Theory
2020-01-14 v1
Abstract
Locally compact abelian groups are classified in which the sum of any two closed subgroups is itself closed. This amounts to reproving and extending results by Yu.~N.~Mukhin from 1970. Namely we contribute a complete classification of all totally disconnected \lca\ groups with closed for any closed subgroups and .
Keywords
Cite
@article{arxiv.1908.08420,
title = {When is the Sum of Two Closed Subgroups Closed in a Locally Compact Abelian Group},
author = {Wolfgang Herfort and Karl H. Hofmann and Francesco G. Russo},
journal= {arXiv preprint arXiv:1908.08420},
year = {2020}
}
Comments
38 pages, 1 figure