可溶性基团的效价

B. A. F. Wehrfritz
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引用次数: 0

摘要

摘要我们特别证明了如果G是一个不存在非平凡局部有限正规子群的可溶群,那么对于G没有正则p截面的每一个素数p, G是幂幂的。(如果对于p的每一个幂n,对于可被n整除的无限阶或有限阶G的任何元素x,存在有限指数G的正规子群n,使得x模n的阶为n,则群G是p幂幂群。一个普适p群是一个无限局部循环的p群。)这推广到一般的可溶群,并对Azarov最近关于多环群和可溶极大极小群的结果给出了更直接的证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Potency in soluble groups
Abstract We prove in particular that if G is a soluble group with no non-trivial locally finite normal subgroups, then G is p-potent for every prime p for which G has no Prüfer p-sections. (A group G is p-potent if for every power n of p and for any element x of G of infinite order or of finite order divisible by n there is a normal subgroup N of G of finite index such that the order of x modulo N is n. A Prüfer p-group is an infinite locally cyclic p-group.) This extends to soluble groups in general, and gives a more direct proof of, recent results of Azarov on polycyclic groups and soluble minimax groups.
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