
This article is cited in 1 scientific paper (total in 1 paper)
Morava $K$theory rings of the extensions of $C_2$ by the products of cyclic $2$groups
Malkhaz Bakuradze^{}, Natia Gachechiladze^{} ^{} Iv. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences
Abstract:
In 2011, Schuster proved that $\mod2$ Morava $K$theory $K(s)^*(BG)$ is evenly generated for all groups $G$ of order $32$. There exist $51$ nonisomorphic groups of order $32$. In a monograph by Hall and Senior, these groups are numbered by $1,…,51$. For the groups $G_{38},…,G_{41}$, which fit in the title, the explicit ring structure is determined in a joint work of M. Jibladze and the author. In particular, $K(s)^*(BG)$ is the quotient of a polynomial ring in 6 variables over $K(s)^*(\mathrm{pt})$ by an ideal generated by explicit polynomials. In this article we present some calculations using the same arguments in combination with a theorem by the author on good groups in the sense of Hopkins–Kuhn–Ravenel. In particular, we consider the groups $G_{36},G_{37}$, each isomorphic to a semidirect product $(C_4\times C_2\times C_2)\rtimes C_2$, the group $G_{34}\cong(C_4\times C_4)\rtimes C_2$ and its nonsplit version $G_{35}$. For these groups the action of $C_2$ is diagonal, i.e., simpler than for the groups $G_{38},…,G_{41}$, however the rings $K(s)^*(BG)$ have the same complexity.
Key words and phrases:
transfer, Morava $K$theory.
DOI:
https://doi.org/10.17323/160945142016164603619
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http://www.mathjournals.org/.../2016016004001.html
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MSC: 55N20, 55R12, 55R40 Received: December 22, 2014; in revised form February 8, 2016
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Citation:
Malkhaz Bakuradze, Natia Gachechiladze, “Morava $K$theory rings of the extensions of $C_2$ by the products of cyclic $2$groups”, Mosc. Math. J., 16:4 (2016), 603–619
Citation in format AMSBIB
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\by Malkhaz~Bakuradze, Natia~Gachechiladze
\paper Morava $K$theory rings of the extensions of $C_2$ by the products of cyclic $2$groups
\jour Mosc. Math.~J.
\yr 2016
\vol 16
\issue 4
\pages 603619
\mathnet{http://mi.mathnet.ru/mmj611}
\crossref{https://doi.org/10.17323/160945142016164603619}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=3598497}
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This publication is cited in the following articles:

M. Bakuradze, N. Gachechiladze, “Some 2groups from the view of Hilbert–Poincaré polynomials of $K(2)^*(BG)$”, Tbil. Math. J., 10:2 (2017), 103–110

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