#### Volume 17, issue 4 (2017)

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On mod $p$ $A_p$–spaces

### Ruizhi Huang and Jie Wu

Algebraic & Geometric Topology 17 (2017) 2125–2144
##### Abstract

We prove a necessary condition for the existence of an ${A}_{p}$–structure on $mod\phantom{\rule{1em}{0ex}}p$ spaces, and also derive a simple proof for the finiteness of the number of $mod\phantom{\rule{1em}{0ex}}p$ ${A}_{p}$–spaces of given rank. As a direct application, we compute a list of possible types of rank $3$ $mod\phantom{\rule{1em}{0ex}}p$ homotopy associative $H$–spaces.

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##### Keywords
$A_p$-space, $\psi$-operation, homotopy associative $H$-space, Steenrod powers, Adem relations
##### Mathematical Subject Classification 2010
Primary: 55P45, 55S25
Secondary: 55N15, 55P15, 55S05