Morava K-theory rings for the groups G_(38),…,G_(41) of order 32

摘要

B. Schuster [19] proved that the mod 2 Morava K-theory K(s)*(BG) is evenly generated for all groups G of order 32. For the four groups G of order 32 with the numbers 38,39,40 and 41 in the Hall-Senior list [11], the ring K(2)*(BG) has been shown to be generated as a K(2)*-module by transferred Euler classes. In this paper, we show this for arbitrary s and compute the ring structure of K(s)*(BG). Namely, we show that K(s)*(BG) is the quotient of a polynomial ring in 6 variables over K(s)*(pt) by an ideal for which we list explicit generators.