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A note on finite groups with the indices of some maximal subgroups being primes | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 6، شماره 2، شهریور 2017، صفحه 17-20 اصل مقاله (163.09 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.12396 | ||
| نویسنده | ||
| Cui Zhang* | ||
| Yantai University | ||
| چکیده | ||
| The Theorem 12 in [A note on $p$-nilpotence and solvability of finite groups, J. Algebra 321 (2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indices. In this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index are solvable. | ||
| کلیدواژه‌ها | ||
| Non-abelian simple group؛ the index of maximal subgroup؛ solvable group | ||
| مراجع | ||
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[1] P. Kleidman and M. Liebeck, The Subgroup Structure of the Finite Classical Groups, London Mathematical Society Lecture Note Series, 129, Cambridge University Press, Cambridge, 1990.
[2] J. S. Rose, On finite insoluble groups with nilpotent maximal subgroups, J. Algebra, 48 (1977) 182–l96.
[3] J. Shi, W. Shi and C. Zhang, A note on p-nilpotence and solvability of finite groups, J. Algebra, 321 (2009) 1555–1560. | ||
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