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

NDERL YING GRUPOIDS

UNDERLYING GRUPOIDS

Murat ALP
Sedat PAK
Pages
239–246
Publication Date
2000-01-15
DOI
—
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AI Summary & Key Takeaways

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

We also made a computational comment on pre-crossed modules, pre-cat Igroups and underlying grupoids in this paper.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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) .
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Conclusion & Impact:We also made a computational comment on pre-crossed modules, pre-cat Igroups and underlying grupoids in this paper.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Crossed modules · Cat'<groups · 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.

Özet

In this paper we describe a package XMOD (Wensley andAlp,1993) of functions for computing with crossed modules, theirmorphisms and derivations; cat' -groups, their morphisms andsections, written using the sf GAP (Schonert , 1993) group theoryprogramming language. We have also enumerated the isomorphismclasses of cat-groups in (Alp ,1997) and (Alp, Wensley ,1997) and(Alp ,1997) We gave the application algorithms and somemathematical results on cat' -group structures in (Alp, 1998) . We alsomade a computational comment on pre-crossed modules, pre-cat Igroupsand underlying grupoids in this paper.

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Cite This Article

ALP, M., PAK, S. (2000). NDERL YING GRUPOIDS. Journal of Scientific Reports-A, Sayı: 001, 239–246. https://ajindex.com/articles/779556

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References (6)

  1. Alp, M., GAP, Crossed modules and Cat61-groups: Applications of computational group theory, University of Wales, Bangor, Ph.D. Thesis, (1997) 440pp. Alp, M., Enumeration of Cat-groups of order 41-47, Anadolu Universitesi Fen Fakiiltesi Dergisi, Sayi 3 (1997) 79-90.
  2. Alp, M., Special cases of Derivations groups, Algebras, Groups and Geometries, Vo1.l5 (J 998) (to appear). Alp, M. and Wensley, C. D., Enumeration of Cati-groups of low order, U. W. B. preprint, 96.05, l5pp. 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.
  3. Loday, J. L., Spaces with finitely many non-trivial homotopy groups, 1.App.Algebra, 24 (1982) J 79-202.
  4. Schonert, M. et ai, GAP: Groups, Algorithms, and Programming, Lehrstuhl D fUr Mathematik, Rheinisch Westfalische Technische Hoch-schule, Aachen, Germany, third edition, 1993.
  5. 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.
  6. Whitehead, J. H. c., On operators in relative homotopy group, Ann. of Math., 49 (1948) 6 J 0-640.