2-Uniform covering groups of elementary abelian 2-groups

Abstract

This article is concerned with the classification of Schur covering groups of the elementary abelian group of order 2 n , up to isomorphism. We consider those covering groups possessing a generating set of n elements having only two distinct squares. We show that such groups may be represented by 2-vertex-colored and 2-edge-colored graphs of order n. We show that in most cases, the isomorphism type of the group is determined by that of the 2-colored graph, and we analyze the exceptions.