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# A new cohomological criterion for the $p$-nilpotence of groups

Published:1998-03-01
Printed: Mar 1998
• Maurizio Brunetti
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## Abstract

Let $G$ be a finite group, $H$ a copy of its $p$-Sylow subgroup, and $\kn$ the $n$-th Morava $K$-theory at $p$. In this paper we prove that the existence of an isomorphism between $K(n)^\ast(BG)$ and $K(n)^\ast(BH)$ is a sufficient condition for $G$ to be $p$-nilpotent.
 MSC Classifications: 55N20 - Generalized (extraordinary) homology and cohomology theories 55N22 - Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]