Vol. 7, No. 1, 2014

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Slide-and-swap permutation groups

Onyebuchi Ekenta, Han Gil Jang and Jacob A. Siehler

Vol. 7 (2014), No. 1, 41–55
Abstract

We present a simple tile-sliding game that can be played on any 3-regular graph, generating a permutation group on the vertices. We classify the resulting permutation groups and obtain a novel presentation for the simple group of 168 elements.

Keywords
simple group, permutation group, primitive group, graph theory
Mathematical Subject Classification 2010
Primary: 20B15, 91A43
Milestones
Received: 16 July 2012
Revised: 10 May 2013
Accepted: 25 May 2013
Published: 24 October 2013

Communicated by Joseph A. Gallian
Authors
Onyebuchi Ekenta
Department of Mathematics
Washington and Lee University
Lexington, VA 24450
United States
Han Gil Jang
Department of Mathematics
Washington and Lee University
Lexington, VA 24450
United States
Jacob A. Siehler