Torsion in H-Spaces II

Characterization of the mod 3 cohomology of $E_7$

“…The starting point of our proof of Theorem 1 is the loop space theorem for odd primes [14]. We recall some results and then we claim that ℘ 3 ℘ 1 H 3 (X; F 3 ) = 0.…”

Homotopy groups and H-maps

“…A result of Lin [9] We will prove the theorem under the conditions stated in (1), the cases (2) implies that fF 2 ifj=l,2A,5,6.…”

Adjoint action of a finite loop space

“…Let [a, b] be a nonzero commutator in the lowest dimension, say m. Since H * (G; F p ) is associative, it follows that a and b are generators and [a, b] is primitive. Then by Theorem 5.4.1 (c) of [6], the m must be odd, and hence, we may assume that a is an even-dimensional generator and b is an odd-dimensional generator. Let us dualize the situation: Let u and v be the dual primitive elements to a and b, and choose x to be a generator such that x, [a, b] = 0.…”