Homotopy groups and H-maps

Abstract

The first nonvanishing homotopy group of a finite H-space X whose mod 2 homology ring is associative occurs in degrees 1, 3 or 7. Generators of these groups can be represented by maps a:S"-*X for n= 1, 3 or 7. In this note we prove that under some hypothesis on X there exists an H-structure on S", n= 1, 3 or 7 such that a is an H-map.