Planar infinite groups
Group Theory
2014-03-04 v1
Abstract
We will determine all infinite -locally finite groups as well as infinite -groups with planar subgroup graph and show that infinite groups satisfying the chain conditions containing an involution do not have planar embeddings. Also, all connected outer-planar groups and outer-planar groups satisfying the chain conditions are presented. As a result, all planar groups which are direct product of connected groups are obtained.
Cite
@article{arxiv.1403.0331,
title = {Planar infinite groups},
author = {Mehdi Rajabian and Mohammad Farrokhi Derakhshandeh Ghouchan and Ahmad Erfanian},
journal= {arXiv preprint arXiv:1403.0331},
year = {2014}
}
Comments
10 pages, 3 figures, To appear in J. Group Theory