Application of crossed modules to GAP (Group, algorithm and programming)

APPLICATIONS OF CROSSED MODULES TO GAP (Group, Algorithm and Programming) Sedat PAK Department of Mathematics, MsC. Thesis, 1999 Thesis Supervisor : Assoc. Prof. Dr. Murat ALP SUMMARY This thesis consists of 5 parts which are respectively: 1. Introduction 2. Crossed modules and Cat1 - groups 3. The kinds of Crossed modules which are Actor,Lue, Whitehead Crossed modules 4. Pullbacks of Crossed modules and Cat1 - groups 5. Manuel for GAP share package XMod. 6. Future of this work Chapter 1 is a brief introduction. Chapter 2 review's the mathematical theory of Crossed modules and their morphism, Cat1 - groups and their morphisms. Some kinds of crossed modules were given in Chapter 3. Pullbacks of crossed modules and Cat1 - groups were investigated in Chapter 4. Chapter 5 contains details of some of the function used in the XMod package for GAP. We discuss some results on Chapter 6 for the future works.