The pronorm of a group G is the set $P(G)$ of all elements $g\in G$ such that X and $X^g$ are conjugate in ${\langle {X,X^g}\rangle }$ for every subgroup X of G. In general the pronorm is not a subgroup, but we give evidence of some classes of groups in which this property holds. We also investigate the structure of a generalised soluble group G whose pronorm contains a subgroup of finite index.

中文翻译：

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在一个小组的pronorm

这代词一组的G是集合$P(G)$所有元素的$g\in G$这样X和$X^g$共轭在${\langle {X,X^g}\rangle }$对于每个子组X的G. 一般来说，代词不是一个子群，但我们给出了该属性在某些类群中成立的证据。我们还研究了广义可溶性基团的结构G其代词包含有限索引的子群。