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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.

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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