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3 results

  • H-Semidirect Products

  • Georg Peschke
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 4 / 01 December 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 402-411
    Print publication:
    01 December 1987
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  • The concept of H-semidirect product structure on a grouplike space is introduced. It is shown that the loop space ΩX of any based CW-complex X is the H-semidirect product of the identity path-component of ΩX with π1,X. The set of free homotopy classes of maps into a Hsemidirect product inherits the structure of a semidirect product. This leads to new results concerning the nilpotency of homotopy classes of maps into a group-like space.

  • Cocyclic Maps and Coevaluation Subgroups

  • K. L. Lim
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 1 / 01 March 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 63-71
    Print publication:
    01 March 1987
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  • For any space X, DG(X, A) is an abelian subgroup of [X, A] when A is an H-group. DG(X, X) is a ring for any H-group X.

  • On Evaluation Subgroups of Generalized Homotopy Groups

  • K. L. Lim
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 1 / 01 March 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 78-86
    Print publication:
    01 March 1984
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  • G(A, X) consists of all homotopy classes of cyclic maps from a space A to another space X. If A is an H-cogroup, then G(A, X) is a group. G(A, X) preserves products in the second variable and is a contravariant functor of A from the full subcategory of H-cogroups and maps into the category of abelian groups and homomorphisms. If X is an H-cogroup, then G(X, X) is a ring.