Morava K -theory rings for the groups G 38 , …, G 41 of order 32

Abstract

B. Schuster (17) proved that the mod 2 Morava K-theory is good in the sense of Hopkins-Kuhn-Ravenel (12) for all 2-groups G of order 32. As for the missing four groups G with the numbers 38, 39, 40 and 41 in the Hall- Senior list (11), Morava K-theory has been shown to be evenly generated and, for s = 2, to be generated by transferred Chern classes. In this paper we compute the ring structure of K(s) � (BG) for these four groups.