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

Abstract

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

23 pages

References in corpus (1)

• Transfer and complex oriented cohomology rings

Cited by in corpus (1)

• Chromatic (co)homology of finite general linear groups