#### Vol. 1, No. 1, 2008

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors’ Interests Scientific Advantages Submission Guidelines Submission Form Ethics Statement Editorial Login Author Index Coming Soon Contacts ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Other MSP Journals
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
Primary: 20M18