Involve: A Journal of Mathematics

  • Involve
  • Volume 7, Number 1 (2014), 41-55.

Slide-and-swap permutation groups

Onyebuchi Ekenta, Han Gil Jang, and Jacob Siehler

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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.

Article information

Involve, Volume 7, Number 1 (2014), 41-55.

Received: 16 July 2012
Revised: 10 May 2013
Accepted: 25 May 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20B15: Primitive groups 91A43: Games involving graphs [See also 05C57]

simple group permutation group primitive group graph theory


Ekenta, Onyebuchi; Jang, Han Gil; Siehler, Jacob. Slide-and-swap permutation groups. Involve 7 (2014), no. 1, 41--55. doi:10.2140/involve.2014.7.41.

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