Monika Truong, On Elementary Properties of Crossed Modules.

Abstract:

A crossed module [[M,G]] consists of two groups M and G, an action of G on M and a group morphism f from M to G that satisfies the conditions (CM1) (m^g)f = (mf)^g and (CM2) m^n = m^{nf}, for m,n in M and g in G. Our goal is to transfer some elementary concepts and assertions from group theory to the theory of crossed modules, such as the Jordan-Hölder Theorem and the Orbit Lemma. Moreover, we reduce the classification problem of simple crossed modules to the classification problem of simple groups.