UNDERLYING GRUPOIDS

Abstract

In this paper we describe a package XMOD (Wensley and

Alp,1993) of functions for computing with crossed modules, their

morphisms and derivations; cat' -groups, their morphisms and

sections, written using the sf GAP (Schonert , 1993) group theory

programming language. We have also enumerated the isomorphism

classes of cat-groups in (Alp ,1997) and (Alp, Wensley ,1997) and

(Alp ,1997) We gave the application algorithms and some

mathematical results on cat' -group structures in (Alp, 1998) . We also

made a computational comment on pre-crossed modules, pre-cat Igroups

and underlying grupoids in this paper.

Keywords

• Crossed modules,Cat'<groups,underlying grupoids

NDERL YING GRUPOIDS

Abstract

In this paper we describe a package XMOD (Wensley and Alp,1993) of functions for computing with crossed modules, their morphisms and derivations; cat' -groups, their morphisms and sections, written using the sf GAP (Schonert , 1993) group theory programming language. We have also enumerated the isomorphism classes of cat-groups in (Alp ,1997) and (Alp, Wensley ,1997) and (Alp ,1997) We gave the application algorithms and some mathematical results on cat' -group structures in (Alp, 1998) . We also made a computational comment on pre-crossed modules, pre-cat Igroups and underlying grupoids in this paper.

Keywords

• Crossed modules
• Cat'<groups
• underlying grupoids

References

1. Alp, M., GAP, Crossed modules and Cat61-groups: Applications of computational group theory, University of Wales, Bangor, Ph.D. Thesis, (1997) 440pp.
2. Alp, M., Enumeration of Cat-groups of order 41-47, Anadolu Universitesi Fen Fakiiltesi Dergisi, Sayi 3 (1997) 79-90.
3. Alp, M., Special cases of Derivations groups, Algebras, Groups and Geometries, Vo1.l5 (J 998) (to appear).
4. Alp, M. and Wensley, C. D., Enumeration of Cati-groups of low order, U. W. B. preprint, 96.05, l5pp.
5. Brown, R. and Higgins, P. J., On the connection between the second relative homotopy group some related space, Proc. London. Math. Soc., 36 (1978) 193-212.
6. Loday, J. L., Spaces with finitely many non-trivial homotopy groups, 1.App.Algebra, 24 (1982) J 79-202.
7. Schonert, M. et ai, GAP: Groups, Algorithms, and Programming, Lehrstuhl D fUr Mathematik, Rheinisch Westfalische Technische Hoch-schule, Aachen, Germany, third edition, 1993.
8. Wensley, C. D., and Alp, M., XMOD, Crossed modules and carl-groups in GAP, version 1.3 Manual for the XMOD share package, (1996) 1-80.

9. Whitehead, J. H. c., On operators in relative homotopy group, Ann. of Math., 49 (1948) 6 J 0-640.