Abstract

A subgroup H of a group G is contranormal if $H^G=G.$ In finite groups, if there are no proper contranormal subgroups, then the group is nilpotent but this is not true in infinite groups as the well-known Heineken–Mohamed groups show. We call such groups without proper contranormal subgroups “contranormal-free.” In this article, we prove various results concerning contranormal-free groups proving, for example that locally generalized radical contranormal-free groups which have finite section rank are hypercentral.

中文翻译：

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一些无异常群的结构

摘要

一个分组ħ一组G ^是contranormal如果$H^G=G.$在有限群中，如果没有合适的逆正规子群，则该群是幂零的，但这在无限群中并非如此，正如著名的 Heineken-Mohamed 群所示。我们称这种没有适当反常子群的群体为“无反常态”。在本文中，我们证明了关于无反常群的各种结果证明，例如具有有限截面秩的局部广义激进无反常群是超中心的。