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K^*(BG) rings for groups G=G38,...,G41G=G_{38},...,G_{41} of order 32

Abstract

B. Schuster \cite{SCH1} proved that the modmod 2 Morava KK-theory K(s)βˆ—(BG)K(s)^*(BG) is evenly generated for all groups GG of order 32. For the four groups GG with the numbers 38, 39, 40 and 41 in the Hall-Senior list \cite{H}, the ring K(2)βˆ—(BG)K(2)^*(BG) has been shown to be generated as a K(2)βˆ—K(2)^*-module by transferred Euler classes. In this paper, we show this for arbitrary ss and compute the ring structure of K(s)βˆ—(BG)K(s)^*(BG). Namely, we show that K(s)βˆ—(BG)K(s)^*(BG) is the quotient of a polynomial ring in 6 variables over K(s)βˆ—(pt)K(s)^*(pt) by an ideal for which we list explicit generators.Comment: 23 page

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