From: Jim Lin <jimlin@math.ucsd.edu>
Date: Thu, 15 Mar 2007 10:15:11 -0700

Don-  Here is a question for the list.  thanks, Jim Lin

Let p be an odd prime.  Given a finite H-space X, it is known that all 
even degree primitives of the mod p homology have height p.   Further, if 
X is homotopy associative, all the odd degree homology primitives occur as 
either odd degree algebra generators or commutators with the even degree 
primitives.
My question is what is known about the mod p homology ring of  nonfinite 
homotopy associative H-spaces?  In particular, consider all the even 
homology primitives of height p in the mod p homology of a nonfinite 
H-space.  Does anyone know examples of such spaces where there are 
commutators of the even degree primitives of height p with other odd 
degree primitives?