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Finite groups with the same conjugacy class sizes as a finite simple group | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 8، شماره 1، خرداد 2019، صفحه 23-33 اصل مقاله (222.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21236 | ||
| نویسنده | ||
| Neda Ahanjideh* | ||
| University of Shahre-kord | ||
| چکیده | ||
| 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 $S$, $G \cong S \times Z(G)$. | ||
| کلیدواژهها | ||
| Prime graph؛ the set of the order components of a finite group؛ the Schur multiplier | ||
| مراجع | ||
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