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Some criteria for solvability and supersolvability | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 425-429 اصل مقاله (456.26 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.20047.1315 | ||
| نویسندگان | ||
| Zohreh Habibi* ؛ Masoomeh Hezarjaribi | ||
| Department of Mathematics, Payame Noor University (PNU), Tehran, Iran | ||
| چکیده | ||
| Denote by $ G $ a finite group, by $ {\rm hsn}(G) $ the harmonic mean Sylow number (eliminating the Sylow numbers that are one) in $G$ and by $ {\rm gsn}(G) $ the geometric mean Sylow number (eliminating the Sylow numbers that are one) in $G$. In this paper, we prove that if either $ {\rm hsn}(G)<45/7 $ or $ {\rm gsn}(G)< \sqrt[3]{300} $, then $G$ is solvable. Also, we show that if either $ {\rm hsn}(G)<24/7 $ or $ {\rm gsn}(G)<\sqrt{12} $, then $G$ is supersolvable. | ||
| کلیدواژه‌ها | ||
| Finite group؛ Sylow subgroup؛ solvable groups | ||
| مراجع | ||
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