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Classification of simply connected and aspherical crossed modules of low order

M. Alp
장전수학회 (Jangjeon Mathematical Society)|2006.10|Advanced Studies in Contemporary Mathematics|제13권 제2호|pp. 255-271

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주제분류수학

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Abstract

In this paper we described a share package XMOD[2] of functions for computing with finite permutation crossed modules, cat-groups and their morphisms, written using the GAP [13] group theory programming language. We also presented actor square of crossed modules which are Lue, Norrie, Whitehead, Actor crossed modules. We gave a list of the simply connected and aspherical crossed modules of the direct products, sub-crossed modules and Factor crossed modules of the above crossed modules.

참고문헌 (15)

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  2. Alp, M., "XMOD - Crossed modules and Cat1-groups in GAP, version 1.3(Manual for the XMOD share package, chapter 73)", pp.1357~1422 (1997)
  3. Alp, M., "Enumeration of cat1-groups of lower order", Int. J. Algebra Comput., 10(4), pp.407~424 (2000)
  4. Brown, R., "On the connection between the second relative homotopy group and some related spaces", Proc. London. Math. Soc., 36, pp.193~212 (1978)
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  10. Lue, A. S. T., "Semi-complete crossed modules and holomorphs of groups", Bull. London Math. Soc., 11, pp.8~16 (1979)
  11. Norrie, K. J., "Actions and automorphisms of crossed modules", Bull. Soc. Math. France, 118, pp.129~146 (1990)
  12. Norrie, K. J., "Crossed module and anologues of group theorems", D, pp.1987
  13. Sch¨onert, M. et al, "Groups, Algorithms, and Programming, 3rd ed" (1993), Lehrstuhl D f¨ur Mathematik, Rheinisch Westf¨alische Technische Hochschule, Aachen, Germany
  14. Whitehead, J. H. C., "Combinatorial homotopy II", Bull. Amer. Math. Soc., 55, pp.453~496 (1949)
  15. Whitehead, J. H. C., "On operators in relative homotopy groups", Ann. Math., 49, pp.610~640 (1948)

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