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首页> 外文期刊>Journal of group theory >Class-preserving automorphisms and the normalizer property for Blackburn groups
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Class-preserving automorphisms and the normalizer property for Blackburn groups

机译：布莱克本群的保留类自同构和规范化属性

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摘要

For a group G, let U be the group of units of the integral group ring ZG. The group G is said to have the normalizer property if N-U(G) = Z(U)G. It is shown that Blackburn groups have the normalizer property. These are the groups which have non-normal finite subgroups, with the intersection of all of them being non-trivial. Groups G for which class-preserving automorphisms are inner automorphisms, Out(c)(G) = 1, have the normalizer property. Recently, Herman and Li have shown that Out(c)(G) = 1 for a finite Blackburn group G. We show that Out(c)(G) = 1 for the members G of certain classes of metabelian groups, from which the Herman-Li result follows. Together with recent work of Hertweck, Iwaki, Jespers and Juriaans, our main result implies that, for an arbitrary group G, the group Z(infinity)(U) of hypercentral units of U is contained in Z(U)G.
机译：对于组G，令U为整数组环ZG的单元组。如果N-U（G）= Z（U）G，则称基团G具有归一化性质。结果表明，Blackburn组具有规范化属性。这些是具有非正规有限子组的组，所有子组的交集都是非平凡的。类别保留自同构是内部自同构，Out（c）（G）= 1的组G具有规格化属性。最近，Herman和Li显示了一个有限的布莱克本群G的Out（c）（G）=1。我们显示了某些类别的变元族G的成员G的Out（c）（G）= 1。 Herman-Li结果如下。连同Hertweck，Iwaki，Jespers和Juriaans的最新工作一起，我们的主要结果表明，对于任意组G，Z（U）G中包含U的超中心单元Z（infinity）（U）。

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