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Geometric Characterization of Property R

William Gordon Ritter
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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.

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William Gordon Ritter. 2004-02-12. Geometric Characterization of Property R. https://arxiv.org/abs/math/0308013

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