On Commutation Semigroups of Dihedral Groups
Rings and Algebras
2013-03-05 v2
Abstract
For G a group and g in G, we define mappings pg(G) and lg(G) from G into G by pg(x)=[x,g] and lg(x)=[g,x]. We let P(G) and L(G) denote the subsemigroups of the set of all mappings from G to G generated by {pg: g in G} and {lg: g in G}, respectively. P(G) and L(G) are called the right and left commutation semigroup of G, respectively. In this paper we will give explicit formulas for the orders of both P(G) and L(G) where G is a dihedral group.
Cite
@article{arxiv.1210.2568,
title = {On Commutation Semigroups of Dihedral Groups},
author = {Darien DeWolf and Charles Edmunds and Christopher Levy},
journal= {arXiv preprint arXiv:1210.2568},
year = {2013}
}