Geometric Characterization of Property R
Group Theory
2007-05-23 v2 Combinatorics
Abstract
Consider pairs of the form (G, N), with G a group and N \normal G, as objects of a category \PG. A morphism (G_1, N_1) \To (G_2, N_2) will be a group homomorphism f : G_1 \To G_2 such that f(N_1) \subset N_2. We introduce a functor Q : \PG \To \Groups, which provides a geometric definition of Property R, since it is most naturally visualized by means of a directed graph. We compute these graphs for a number of finite groups of small order, and prove a general characterization of the graphs which occur in this way.
Cite
@article{arxiv.math/0308013,
title = {Geometric Characterization of Property R},
author = {William Gordon Ritter},
journal= {arXiv preprint arXiv:math/0308013},
year = {2007}
}
Comments
8 pages, 4 figures