On groups with Cayley graph isomorphic to a cube

Details On groups with Cayley graph isomorphic to a cube On groups with Cayley graph isomorphic to a cube

2011-11-10

arxiv.org/abs/1111.2570v2

Mathematics

Group Theory

9 pages, 4 figures, replaced Theorem 3.1 with a more general version that holds for any p-group

Scientific paper

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.

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