%0 Journal Article
%T On groups with Cayley graph isomorphic to a cube
%A Colin Hagemeyer
%A Richard Scott
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1111.2570v2