A practical method for enumerating cosets of a finite abstract group

Abstract

An important problem in finite-group theory is the determination of an abstract definition for a given group , that is, a set of relationsbetween k generating operations S1, …., Sk of , such that every other relation between S1, …., Sk is an algebraic consequence of (1).The number of groups for which abstract definitions are actually known is relatively small, but a remarkable feature of the results already obtained is the extreme simplicity of the relations (1) in the case of several groups of quite high order. This fact constitutes an additional incentive to the search for abstract definitions, and many elegant results have doubtless yet to be discovered.