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

Zhang, Cui

doi:10.22108/ijgt.2017.12396

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

Document Type : Research Paper

Author

Cui Zhang

Yantai University

10.22108/ijgt.2017.12396

Abstract

‎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.

Keywords

20.1001.1.22517650.2017.6.2.3.6

Main Subjects

20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks

References

[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.