Computing 3-Dimensional Groups : Crossed Squares and Cat$^2$-Groups

Abstract

The category XSq of crossed squares is equivalent to the category Cat2 of cat 2 -groups. Functions for computing with these structures have been developed in the package XMod written using the GAP computational discrete algebra programming language. This paper includes details of the algorithms used. It contains tables listing the 1, 000 isomorphism classes of cat 2 -groups on groups of order at most 30.