Operations on locally free classgroups

群环中的几乎平凡单位

Almost Trivial Units in Group Rings

本文确定了所有使群环具有几乎平凡单位的整数环与有限群，并计算了相应群环的Swan子群。

Bloch-Kato pro-p groups and locally powerful groups

A Bloch-Kato pro-p group G is a pro-p group with the property that the F_p-cohomology ring of every closed subgroup of G is quadratic. It is shown that either such a pro-p group G contains no closed free pro-p groups of infinite rank, or there exists an orientation $θ\colon G\rightarrow \Z_p^\times$ such that G is theta-abelian. In case that G is also finitely generated, this implies that G is powerful, p-adic analytic with d(G)=cd(G), and its \F_p-cohomology ring is an exterior algebra. These results will be obtained by studying locally powerful groups (see Theorem A). There are certain Galoi…