Planar infinite groups
  We will determine all infinite $2$-locally finite groups as well as infinite $2$-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. 
Mehdi Rajabian, Mohammad Farrokhi Derakhshandeh Ghouchan and Ahmad   Erfanian
math.GR