Journals / Journal of Scientific Reports-A / 2000 / Sayı: 001

SECTIONS IN GAP

Pages
225–238
Publication Date
2000-01-15
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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).

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:We also give the implementation method of sections to the CAP. /991 A.
💡
Conclusion & Impact: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).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:section · gap · Crossed modules

Abstract

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).

Özet

In this paper we describe a share package XMOD (Alp,Wensley, 1997) of functions for computing with finite, permutationcrossed modules, their morphisms and derivations; cat'<groups, theirmorphisms and their sections, written using the CAP (Schonert, /993)group theory programming language. We also give theimplementation 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.

🔖

Cite This Article

ALP, M., PAK, S. (2000). SECTIONS IN GAP. Journal of Scientific Reports-A, Sayı: 001, 225–238. https://ajindex.com/articles/779555

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  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. Ellis, G_ J-, Crossed modules and their higher dimensional analogues, Ph.D thesis, Univ. of Wales, Bangor, (1984).
  5. Loday, J. L, Spaces with finitely many non-trivial homotopy groups, J.App.Algebra, 24 (1982) 179-202.
  6. Whitehead, J. H_ c., Combinatorial homotopy II, Bull. A.M.S., 55 (1949) 453- 496. Lue, A. S. T., Semi-complete crossed modules and holomorphs of groups, Bull. London Math. Soc., II (1979) 8-16.
  7. Lue, A. S. T., The centre of the outer automorphism group of a free group, Bull. London Math. Soc., II (1979) 6-7.
  8. Norrie, K. J., Crossed module and anologues of group theorems, Ph.D thesis, Kings College, University of London, (1987).
  9. Gilbert, N.D., Derivations, automorphisms and crossed modules, Comm. in Algebra 18:2703--2734, 1990.
  10. Alp, M. GAP Crossed Modules, Catl-groups to the Computational Group theory, PhD Thesis, University of Wales, Bangor. 1997
  11. Alp, M. and Wensley C. D., Enumeration of Catl-groups of Lower order groups, IJAC. 1999.
  12. Alp, M. Pullback Cat I-groups, Turkish Journal of Mathematics 1998
  13. Alp, M. Left Adjoint of Pullback Catl-groups, Turkish Journal of Mathematics, 1998