On groups with Cayley graph isomorphic to a cube
Group Theory
2012-01-13 v2
Abstract
We say that a group G is a cube group if it is generated by a set S of involutions such that the corresponding Cayley graph Cay(G,S) is isomorphic to a cube. Equivalently, G is a cube group if it acts on a cube such that the action is simply-transitive on the vertices and the edge stabilizers are all nontrivial. The action on the cube extends to an orthogonal linear action, which we call the geometric representation. We prove a combinatorial decomposition for cube groups into products of 2-element subgroup, and show that the geometric representation is always reducible.
Cite
@article{arxiv.1111.2570,
title = {On groups with Cayley graph isomorphic to a cube},
author = {Colin Hagemeyer and Richard Scott},
journal= {arXiv preprint arXiv:1111.2570},
year = {2012}
}
Comments
9 pages, 4 figures, replaced Theorem 3.1 with a more general version that holds for any p-group