The main purpose of this paper is to study groups $G_1$, $G_2$ such that $H^\ast(BG_1,{\bf Z}/p)$ is isomorphic to $H^\ast(BG_2,{\bf Z}/p)$ in ${\cal U}$, the category of unstable modules over the Steenrod algebra ${\cal A}$, but not isomorphic as graded algebras over ${\bf Z}/p$.

MSC Classifications:

55R35, 20J06 show english descriptions Classifying spaces of groups and $H$-spaces
Cohomology of groups 55R35 - Classifying spaces of groups and $H$-spaces
20J06 - Cohomology of groups

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