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Abstract

It is known that the order of all Postnikov $k$-invariants of an H-space of finite type is finite. This paper establishes the finiteness of the order of the $k$-invariants $k^{m+1}(X)$ of $X$ in dimensions $m ≤ 2n$ if $X$ is an $(n-1)$-connected H-space which is not necessarily of finite type $(n ≥ 1)$. Similar results hold more generally for higher k-invariants if $X$ is an iterated loop space. Moreover, we provide in all cases explicit universal upper bounds for the order of the k-invariants of $X$.