Some criteria for solvability and supersolvability
عنوان مقاله: Some criteria for solvability and supersolvability
شناسه ملی مقاله: JR_KJMMRC-12-2_028
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_KJMMRC-12-2_028
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
Zohreh Habibi - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
Masoomeh Hezarjaribi - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
خلاصه مقاله:
Zohreh Habibi - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
Masoomeh Hezarjaribi - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
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)<۴۵/۷ or {\rm gsn}(G)< \sqrt[۳]{۳۰۰} , then G is solvable. Also, we show that if either {\rm hsn}(G)<۲۴/۷ or {\rm gsn}(G)<\sqrt{۱۲} , then G is supersolvable.
کلمات کلیدی: Finite group, Sylow subgroup, solvable groups
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1667452/