P-primary decomposition of maps into an H-space

Albert Oscar Shar

Vol. 59 (1975), No. 1, 237–240

DOI: 10.2140/pjm.1975.59.237

Abstract

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 1_∗⁻¹(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

Milestones

Received: 7 January 1975

Revised: 6 March 1975

Published: 1 July 1975