A property of the lamplighter group

Abstract

We show that the inert subgroups of the lamplighter group fall into exactly five commensurability classes. The result is then connected with the theory of totally disconnected locally compact groups and with algebraic entropy.

Keywords

• lamplighter group
• commensurate subgroups
• inert subgroups
• intrinsic dimension entropy
• primary 16d10
• secondary 16e50, 16e20