# The Finite Lamplighter Groups: A Guided Tour

by Jacob Siehler

Year of Award: 2013

Award: Pólya Award

Publication Information: The College Mathematics Journal, Vol. 43, no. 3, May 2012, pp. 203-211.

Summary: (Adapted from the MathFest 2013 Prizes and Awards Booklet) The finite lamplighter group $$L_n$$ has $$n$$ lamps arranged in a circle with a lighting mechanism. An operation consists of rotating the lighter and then possibly toggling one of the lamps on-off. These groups provide examples of nonabelian groups just a touch beyond the dihedral groups.