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2008 Maximal subgroups of the semigroup of partial symmetries of a regular polygon
Thomas Shelly, Janet Mills
Involve 1(1): 33-45 (2008). DOI: 10.2140/involve.2008.1.33

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.

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Thomas Shelly. Janet Mills. "Maximal subgroups of the semigroup of partial symmetries of a regular polygon." Involve 1 (1) 33 - 45, 2008. https://doi.org/10.2140/involve.2008.1.33

Information

Received: 11 June 2007; Accepted: 1 November 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1148.20048
MathSciNet: MR2403065
Digital Object Identifier: 10.2140/involve.2008.1.33

Subjects:
Primary: 20M18

Keywords: polygon , semigroup , symmetries

Rights: Copyright © 2008 Mathematical Sciences Publishers

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