English

Planar infinite groups

Group Theory 2014-03-04 v1

Abstract

We will determine all infinite 22-locally finite groups as well as infinite 22-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.

Keywords

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

R2 v1 2026-06-22T03:18:49.476Z