A note on finite groups with the indices of some maximal subgroups being primes

Document Type : Research Paper


Yantai University


‎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.


Main Subjects

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[3] J. Shi, W. Shi and C. Zhang, A note on p-nilpotence and solvability of finite groups, J. Algebra, 321 (2009)