Mod 3 cohomology algebras of finite H-spaces

Let X be a 3 local, finite, simply connected H-space with associative homology ring . Some known examples are the Lie group , Harper's H-space X(3) and any odd dimensional sphere . We prove the cohomology algebra is isomorphic to the cohomology algebra of a finite product of and odd dimensional spheres. Received: 15 May 2001; in final form: 22 May 2001 / Published online: 28 February 2002