Mehdi Rajabian, Mohammad Farrokhi D. G., Ahmad Erfanian
April 3, 2014

### Abstract

We will determine all infinite 2-locally finite groups and all infinite 2-groups with planar subgroup graph, and show that infinite groups that satisfy the chain conditions and contain an involution do not have planar embeddings. We also determine all connected outer-planar groups and outer-planar groups satisfying the chain conditions. As a result, we obtain all planar groups that are direct products of connected groups.