SECTIONS IN GAP

Yıl 2000, Sayı: 001, 225 - 238, 15.01.2000

Murat Alp Sedat Pak

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

• 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.
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• Whitehead, J. H_ c., On adding relations to homotopy groups, Ann. Math., 47 (1946) 806-810.
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• Alp, M. GAP Crossed Modules, Catl-groups to the Computational Group theory, PhD Thesis, University of Wales, Bangor. 1997
• Alp, M. and Wensley C. D., Enumeration of Catl-groups of Lower order groups, IJAC. 1999.
• Alp, M. Pullback Cat I-groups, Turkish Journal of Mathematics 1998
• Alp, M. Left Adjoint of Pullback Catl-groups, Turkish Journal of Mathematics, 1998