具有与有限单群相同共轭类大小的有限群

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2017-03-04 DOI:10.22108/IJGT.2017.21236

N. Ahanjideh

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引用次数: 5

摘要

对于有限群$H$ $，设$cs(H)$表示$H$的非平凡共轭类大小的集合，$OC(H)$为$H$ $的阶分量的集合。在本文中，我们证明了如果$S$是具有连通素数图的有限简单群，$G$是满足$cs(S)=cs(G)$ $的有限群，则$|S|=|G/Z(G)|$和$OC(S)=OC(G/Z(G))$ $。特别地，我们证明了对于某些有限简单群$S$， $G长S乘以Z(G)$。

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Finite groups with the same conjugacy class sizes as a finite simple group

For a finite group $H$‎, ‎let $cs(H)$ denote the set of non-trivial conjugacy class sizes of $H$ and $OC(H)$ be the set of the order components of $H$‎. ‎In this paper‎, ‎we show that if $S$ is a finite simple group with the disconnected prime graph and $G$ is a finite group such that $cs(S)=cs(G)$‎, ‎then $|S|=|G/Z(G)|$ and $OC(S)=OC(G/Z(G))$‎. ‎In particular‎, ‎we show that for some finite simple group $S$‎, ‎$G cong S times Z(G)$‎.

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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.