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首页> 外文期刊>Moscow mathematical journal >MORAVA K-THEORY RINGS OF THE EXTENSIONS OF C-2 BY THE PRODUCTS OF CYCLIC 2-GROUP
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MORAVA K-THEORY RINGS OF THE EXTENSIONS OF C-2 BY THE PRODUCTS OF CYCLIC 2-GROUP

机译:环2-基团产物对C-2延伸的Morava K-理论环

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摘要

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 G(38), . . . , G(41), which fit in the title, the explicitring 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 G(36), G(37), each isomorphic to a semidirect product (C-4 x C-2 x C-2) x(sic) C-2, the group G34 congruent to (C-4 x C-4) x(sic) C-2 and its non-split version G(35). For these groups the action of C-2 is diagonal, i.e., simpler than for the groups G(38), . . . ,G(41), however the rings K(s)*(BG) have the same complexity.
机译:2011年,舒斯特尔证明,阶32的所有G组均均匀生成mod 2 Morava K-理论K(s)*(BG)。存在51个阶32的非同构群。在霍尔和高级专着中,这些组用1编号。 。 。 ,51.对于组G(38),。 。 。 ,G(41),适合标题,显式结构由M. Jibladze和作者共同确定。特别地,K(s)*(BG)是多项式环在K(s)*(pt)上的6个变量中的商与显式多项式生成的理想值的商。在本文中,我们使用Hopkins-Kuhn-Ravenel的意义上的相同组,结合作者对良好群的一个定理,给出了一些计算。特别是,我们考虑G(36),G(37)组,每个同构为半直接乘积(C-4 x C-2 x C-2)x(sic)C-2,G34组与( C-4 x C-4)x(sic)C-2及其非拆分版本G(35)。对于这些组,C-2的作用是对角线的,即比对于组G(38),...更简单。 。 。 ,G(41),但是环K(s)*(BG)具有相同的复杂度。

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