SECTIONS IN GAP

Öz

In this paper we describe a share package XMOD (Alp,

Wensley, 1997) of functions for computing with finite, permutation

crossed modules, their morphisms and derivations; cat'<groups, their

morphisms and their sections, written using the CAP (Schonert, /993)

group theory programming language. We also give the

implementation method of sections to the CAP.

/991 A. M. S. c. 13D99, 16A99, 17899, 17D99, 18D35.

Keywords: Crossed modules, derivation, whitehead multiplication,

Cat'<groups.sections.

Anahtar Kelimeler

• section,gap

SECTIONS IN GAP

Öz

In this paper we describe a share package XMOD (Alp, Wensley, 1997) of functions for computing with finite, permutation crossed modules, their morphisms and derivations; cat'morphisms and their sections, written using the CAP (Schonert, /993) group theory programming language. We also give the implementation method of sections to the CAP. /991 A. M. S. c. 13D99, 16A99, 17899, 17D99, 18D35. ,>A starting point for this paper was to consider the possibility of implementing functions for doing calculations with crossed modules, derivations, actor crossed modules, catl-groups, sections, induced crossed modules and induced cat I-groups in GAP (Schonert, I993).

Anahtar Kelimeler

• Crossed modules
• derivation
• whitehead multiplication
• Cat'<groups.sections.

Kaynakça

1. Alp, M., and Wensley, C. D., XMOD, Crossed modules and cat l-groups in GAP, version 1.3 Manual for the XMOD share package, (1996) 1-80.
2. Schonert, M. et aI, GAP: Groups, Algorithms, and Programming, Lehrstuhl D fiir Mathematik, Rheinisch Westf a lische Technische Hochschule, Aachen, Germany, third edition, 1993.
3. Brown, R. and Higgins, P. J., On the connection between the second relative homotopy groups of some related spaces, Proc. London Math. Soc., (3) 36 (1978) 193-212.
4. Whitehead, J. H_ c., On adding relations to homotopy groups, Ann. Math., 47 (1946) 806-810.
5. Ellis, G_ J-, Crossed modules and their higher dimensional analogues, Ph.D thesis, Univ. of Wales, Bangor, (1984).
6. Loday, J. L, Spaces with finitely many non-trivial homotopy groups, J .App.Algebra, 24 (1982) 179-202.
7. Whitehead, J. H_ c., Combinatorial homotopy II, Bull. A.M.S., 55 (1949) 453- 496.
8. Lue, A. S. T., Semi-complete crossed modules and holomorphs of groups, Bull. London Math. Soc., II (1979) 8-16.

9. Lue, A. S. T., The centre of the outer automorphism group of a free group, Bull. London Math. Soc., II (1979) 6-7.
10. Norrie, K. J., Crossed module and anologues of group theorems, Ph.D thesis, Kings College, University of London, (1987).
11. Gilbert, N.D., Derivations, automorphisms and crossed modules, Comm. in Algebra 18:2703--2734, 1990.
12. Alp, M. GAP Crossed Modules, Catl-groups to the Computational Group theory, PhD Thesis, University of Wales, Bangor. 1997
13. Alp, M. and Wensley C. D., Enumeration of Catl-groups of Lower order groups, IJAC. 1999.
14. Alp, M. Pullback Cat I-groups, Turkish Journal of Mathematics 1998
15. Alp, M. Left Adjoint of Pullback Catl-groups, Turkish Journal of Mathematics, 1998