在有限幂零无限群上

IF 0.7 Q2 MATHEMATICS
E. Detomi, M. Morigi
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引用次数: 0

摘要

设$gamma_n=[x_1,ldots,x_n]$为第n个中下单词。假设$G$是一个无限群,其中共轭类$x^{gamma_n(G)}$包含小于$2^{aleph_0}$ $的元素。我们证明了$gamma_{n+1}(G)$具有有限阶。这推广了著名的定理B。‎‎。Neumann认为bfc群的换向子群是有限的。而且,它暗示了一个无限群$G$是幂零有限的当且仅当存在一个正整数$n$使得$x^{gamma_n(G)}$包含少于$2^{aleph_0}$ $的元素,对于任意$ xing $ $ $。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On finite-by-nilpotent profinite groups
Let $gamma_n=[x_1,ldots,x_n]$ be the $n$th lower central word‎. ‎Suppose that $G$ is a profinite group‎ ‎where the conjugacy classes $x^{gamma_n(G)}$ contains less than $2^{aleph_0}$‎ ‎elements‎ ‎for any $x in G$‎. ‎We prove that then $gamma_{n+1}(G)$ has finite order‎. ‎This generalizes the much celebrated‎ ‎theorem of B‎. ‎H‎. ‎Neumann that says that the commutator subgroup of a BFC-group is finite‎. ‎Moreover‎, ‎it implies that‎ ‎a profinite group $G$ is finite-by-nilpotent if and only if there is a positive integer $n$ such that‎ ‎$x^{gamma_n(G)}$ contains less than $2^{aleph_0}$‎ ‎elements‎, ‎for any $xin G$‎.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
1
审稿时长
30 weeks
期刊介绍: International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.
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