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The Morava $ K$-theories of some classifying spaces


Author: Nicholas J. Kuhn
Journal: Trans. Amer. Math. Soc. 304 (1987), 193-205
MSC: Primary 55N22; Secondary 19L99
DOI: https://doi.org/10.1090/S0002-9947-1987-0906812-8
MathSciNet review: 906812
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Abstract: Let $ P$ be a finite abelian $ p$-group with classifying space $ BP$. We compute, in representation theoretic terms, the Morava $ K$-theories of the stable wedge summands of $ BP$. In particular, we obtain a simple, and purely group theoretic, description of the rank of $ K{(s)^{\ast}}(BG)$ for any finite group $ G$ with an abelian $ p$-Sylow subgroup. A minimal amount of topology quickly reduces the problem to an algebraic one of analyzing truncated polynomial algebras as modular representations of the semigroup $ {M_n}({\mathbf{Z}} / p)$.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0906812-8
Article copyright: © Copyright 1987 American Mathematical Society

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