A Jordan-H¨older Theorem for Crossed Squares

Abstract

In this study, we focus on the decomposition of a crossed square via its composition series by generalizing the Jordan-Hölder's uniqueness theorem for groups. For this purpose, we discuss and modify the normality conditions on subcrossed squares and also extend some results such as the isomorphism theorems, the Zassenhaus (butterfly) lemma and the Schreier refinement theorem to crossed squares.