A note on finite groups with the indice 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

[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)