具有唯一非幂零固有子群的有限群的性质

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2019-08-14 DOI:10.22108/IJGT.2019.116209.1543

B. Taeri, Fatemeh Tayanloo-Beyg

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引用次数: 0

摘要

我们用一个唯一的非幂零真子群刻画了有限非幂零群$G$。我们证明$|G|$最多有三个质因数。当$G$是超可解的，我们得到$G$的表示;当$G$是不可解的，我们证明$G$是Schmidt群与一个循环群的直接积，或者是$p$-群与一个素数幂次的循环群的半直接积。

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Characterization of finite groups with a unique non-nilpotent proper subgroup

‎‎We characterize finite non-nilpotent groups $G$ with a unique non-nilpotent proper subgroup‎. ‎We show that $|G|$ has at most‎ ‎three prime divisors‎. ‎When $G$ is supersolvable we find the presentation of $G$ and when $G$ is non-supersolvable we show that‎ ‎either $G$ is a direct product of an Schmidt group and a cyclic group or a semi direct product of a $p$-group by a cyclic group of prime power order‎.

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来源期刊

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

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.