Previous issue ·  Next issue ·  Recently posted articles ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Moscow Mathematical Journal

Volume 16, Issue 4, October–December 2016  pp. 603–619.

Morava K-theory rings of the extensions of C2 by the products of cyclic 2-groups

Authors:  Malkhaz Bakuradze (1) and Natia Gachechiladze (1)
Author institution:(1) Iv. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences


In 2011, Schuster proved that mod 2 Morava K-theory K(s)*(BG) is evenly generated for all groups G of order 32. There exist 51 non-isomorphic groups of order 32. In a monograph by Hall and Senior, these groups are numbered by 1, ..., 51. For the groups G38, ..., G41, 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)*(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 G36, G37, each isomorphic to a semidirect product (C4×C2×C2) ⋊ C2 , the group G34 ≅ (C4×C4) ⋊ C2 and its non-split version G35. For these groups the action of C2 is diagonal, i.e., simpler than for the groups G38, ..., G41, however the rings K(s)*(BG) have the same complexity.

2010 Math. Subj. Class. 55N20; 55R12; 55R40.

Keywords: Transfer, Morava K-theory.

Contents   Full-Text PDF