English

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 X+YX+Y closed for any closed subgroups XX and YY.

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