|
|||||
 |
|
|
|
|
|
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 is the collection of all distance-preserving bijections between subpolygons of , 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 . In this paper we construct all of the maximal subgroups that can occur for any regular polygon , and determine for which 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 |
|
|
