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Odd-degree elements in the Morava $$K(n)$$ cohomology of finite groups. (English) Zbl 0963.55004
In an earlier paper [Topology 36, No. 6, 1247-1273 (1997; Zbl 0896.55005)] the first author showed that the second Morava $$K$$-theory of the classifying space of the $$3$$-Sylow subgroup of $$GL_4({\mathbb Z}/3)$$ is nontrivial in odd degrees, thus resolving a question asked by M. J. Hopkins, N. J. Kuhn and D. C. Ravenel [Lect. Notes Math. 1509, 186-209 (1992; Zbl 0757.55006)]. The paper under review extends these results to show that $$K(n)^*(BP)$$ has nontrivial odd degree elements for all $$n \geq 2$$, and all odd primes when $$P$$ is the $$p$$-Sylow subgroup of $$GL_4({\mathbb F}_p)$$ and $$BP$$ is its classifying space.

##### MSC:
 55N22 Bordism and cobordism theories and formal group laws in algebraic topology 55R40 Homology of classifying spaces and characteristic classes in algebraic topology
Morava K-theory
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