Vol. 1, No. 1, 2008

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Maximal subgroups of the semigroup of partial symmetries of a regular polygon

Thomas L. Shelly and Janet E. Mills

Vol. 1 (2008), No. 1, 33–45
Abstract

The semigroup of partial symmetries of a polygon P is the collection of all distance-preserving bijections between subpolygons of P, with composition as the operation. Around every idempotent of the semigroup there is a maximal subgroup that is the group of symmetries of a subpolygon of P. In this paper we construct all of the maximal subgroups that can occur for any regular polygon P, and determine for which P there exist nontrivial cyclic maximal subgroups, and for which there are only dihedral maximal subgroups.

Keywords
semigroup, polygon, symmetries
Mathematical Subject Classification 2000
Primary: 20M18
Milestones
Received: 11 June 2007
Accepted: 1 November 2007
Published: 28 February 2008

Communicated by Scott Chapman
Authors
Thomas L. Shelly
Department of Mathematics
901 12th Ave.
P.O. Box 222000
Seattle, WA 98122-1090
United States
Janet E. Mills
Department of Mathematics
901 12th Ave.
P.O. Box 222000
Seattle, WA 98122-1090
United States