Slide-and-swap permutation groups

Ekenta, Onyebuchi; Jang, Han Gil; Siehler, Jacob

doi:10.2140/involve.2014.7.41

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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

DOI: 10.2140/involve.2014.7.41

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

Vol. 7, No. 1, 2014