Open Access
March 2020 All extensions of $C_2$ by $C_{2^n} \times C_{2^n}$ are good for the Morava $K$-theory
Malkhaz Bakuradze
Hiroshima Math. J. 50(1): 1-15 (March 2020). DOI: 10.32917/hmj/1583550012


Let $C_m$ be a cyclic group of order $m$. We prove that if a group $G$ fits into an extension $1 \rightarrow C^2_{2^{n+1}} \rightarrow G \rightarrow C_2 \rightarrow 1$ for $n\geq 1$ then $G$ is good in the sense of Hopkins-Kuhn-Ravenel, i.e., $K(s)^\ast(BG)$ is evenly generated by transfers of Euler classes of complex representations of subgroups of $G$.

Funding Statement

The author is supported by Shota Rustaveli National Science Foundation Grant 217-614 and CNRS PICS Grant 7736.


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Malkhaz Bakuradze. "All extensions of $C_2$ by $C_{2^n} \times C_{2^n}$ are good for the Morava $K$-theory." Hiroshima Math. J. 50 (1) 1 - 15, March 2020.


Received: 26 April 2017; Revised: 14 June 2019; Published: March 2020
First available in Project Euclid: 7 March 2020

zbMATH: 07197867
MathSciNet: MR4074376
Digital Object Identifier: 10.32917/hmj/1583550012

Primary: 55N20
Secondary: 55R12 , 55R40

Keywords: Euler class , Morava $K$-theory , transfer

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

Vol.50 • No. 1 • March 2020
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