On 𝐻-spaces \modℭ_{𝔭}

Haslam, H. B.

doi:10.1090/S0002-9939-1971-0310870-5

On $H$-spaces $\mod \mathfrak {C}_p$
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Proc. Amer. Math. Soc. 30 (1971), 383-387 Request permission

Abstract:

We show that if a space X is an H-space ${\bmod \; \mathfrak {C}_p}$, then X is “dominated” by the reduced product space ${X_\infty }( = \Omega \Sigma X)$ of X and also by the component of the identity map in the space of all maps from X to X. We then deduce algebraic facts about the suspension homomorphism and the homomorphisms induced by the evaluation map. Making use of a new and pretty result of S. Weingram we give a short proof of the result of W. Browder that the $\bmod \;p$ Hurewicz homomorphism is zero in even dimensions for an H-space $\bmod \; {\mathfrak {C}_p}$.

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