The vanishing of Steenrod squares on H-spaces
Let X be a simply connected finite H-space whose mod 2 homology is an associative ring. The author shows that for \(r\geq 0\) and \(k>0\) \[ QH^{2^ r+2^{r+1}k-1}(X)\subseteq Sq^{2^ r}H^*(\Omega X) \] and \[ Sq^{2^ r}QH^{2^ r+2^{r+1}k-1}(X)=0 \] and concludes that many Steenrod operations take indecomposables to decomposables. The primitively generated case of this result was proved by \textit{E. Thomas} [Ann. Math., II. Ser. 77, 306-317 (1963; Zbl 0115.403) and ibid. 81, 473-495 (1965; Zbl 0127.135)].
scientific article; zbMATH DE number 4080414