Enumerating maximal-order abelian groups within a set of eligible elements

Abstract

An implicit enumeration algorithm for finding maximal-order abelian groups contained within a set of potential group elements is described. The problem of finding such groups arises in the area of experimental design when certain symmetrical fractional factorials are desired. Simple complete enumeration algorithms are inefficient in the sense that each distinct group is generated more than once. The proposed algorithm utilizes a system of flags in conjunction with a subset selection procedure such that each distinct group is generated exactly once. The algorithm is applied to problems in the design of experiments, and solutions are presented.