Some results on the join graph of finite groups
Publish place: International Journal of Group Theory، Vol: 10، Issue: 4
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_THEGR-10-4_003
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
Let $G$ be a finite group which is not cyclic of prime power order. The join graph $\Delta(G)$ of $G$ is a graph whose vertex set is the set of all proper subgroups of $G$, which are not contained in the Frattini subgroup $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $G=\langle H, K\rangle$. Among other results, we show that if $G$ is a finite cyclic group and $H$ is a finite group such that $\Delta(G)\cong\Delta(H)$, then $H$ is cyclic. Also we prove that $\Delta(G)\cong\Delta(A_۵)$ if and only if $G\cong A_۵$.
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Authors
Zahara Bahrami
Department of Mathematical Sciences, Isfahan University of Technology, P.O.Box ۸۴۱۵۶-۸۳۱۱۱, Isfahan, Iran
Bijan Taeri
Department of Mathematical Sciences, Isfahan University of Technology, P.O.Box ۸۴۱۵۶-۸۳۱۱۱, Isfahan, Iran