Mackay Groups and Their Applications

Mackay groups (or compound groups) are considered in the historical context, as one of two possible kinds of multiple antisymmetry. The number of junior Mackay groups of M^m type is calculated for different nonisomorphic antisymmetric characteristics formed by 1 l 4 generators. Combinatorial relationships connecting Mackay and Zamorzaev multiple antisymmetry groups are established. Geometrical applications of Mackay groups making possible direct dimensional transition from n-dimensional symmetry groups to (n + 2) dimensional subperiodic symmetry groups are discussed. Some open problems connected with Mackay groups are given.