Vol. 59, No. 1, 1975

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P-primary decomposition of maps into an H-space

Albert Oscar Shar

Vol. 59 (1975), No. 1, 237–240

If Y is a finitely generated homotopy associative H-space and X is finite CW then [X,Y ] is a nilpotent group. Using this it is easy to show that for any set of prime integers P, a localization map I: Y Y P induces l[X,Y ] [X,Y P] with the order of 11(α) prime to P. (e.g. see [2]) Since there is no theory of the localization of algebraic loops the same technique does not apply if Y is not homotopy associative. The purpose of this paper is to show that the above theorem holds in this situation.

Mathematical Subject Classification
Primary: 55D45
Received: 7 January 1975
Revised: 6 March 1975
Published: 1 July 1975
Albert Oscar Shar