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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.

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About the Author: (From the MathFest 2013 Prizes and Awards Booklet)

Jacob Siehler received his B.S. in mathematics and computer science at Frostburg State University, and his PhD. in mathematics from Virginia Tech, where he studied topological quantum field theories with Frank Quinn. From there, he went to Washington & Lee University where he taught until 2012. He lives near Lexington, Virginia with a Belgian sheepdog who has never been employed to grade Siehler's calculus homework for him, despite the rumors.

Subject classification(s): Algebra and Number Theory | Abstract Algebra | Groups
Publication Date: 
Thursday, August 22, 2013