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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On $ H$-spaces $ \mod \mathfrak{C}_p$


Author: H. B. Haslam
Journal: Proc. Amer. Math. Soc. 30 (1971), 383-387
MSC: Primary 55D45
DOI: https://doi.org/10.1090/S0002-9939-1971-0310870-5
MathSciNet review: 0310870
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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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DOI: https://doi.org/10.1090/S0002-9939-1971-0310870-5
Keywords: H-space, H-space $ \bmod \; {\mathfrak{C}_p}$, Serre classes, suspension homomorphism, Hurewicz homomorphism
Article copyright: © Copyright 1971 American Mathematical Society

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