## Illinois Journal of Mathematics

### Regularity of finite $H$-spaces

John R. Harper

#### Abstract

Let $X$ be an $H$-space of the homotopy type of a connected finite CW complex. Suppose the generators of the rational cohomology of $X$ all have dimension $\leq m$. Theorem. If $p$ is a prime satisfying $2p-1\geq m$, then $X$ is mod $p$ equivalent to a product of odd dimensional spheres and generalized Lens spaces $L(p,1,\ldots,1)$ obtained as the orbit space of an action of $Z_{\mathrm{p}}$ on $S^{2\mathrm{p}-1}$.

#### Article information

Source
Illinois J. Math., Volume 23, Issue 2 (1979), 330-333.

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256048244

Digital Object Identifier
doi:10.1215/ijm/1256048244

Mathematical Reviews number (MathSciNet)
MR528568

Zentralblatt MATH identifier
0409.55007

Subjects
Primary: 55P45: $H$-spaces and duals

#### Citation

Harper, John R. Regularity of finite $H$-spaces. Illinois J. Math. 23 (1979), no. 2, 330--333. doi:10.1215/ijm/1256048244. https://projecteuclid.org/euclid.ijm/1256048244