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

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

• Non-abelian simple group
• the index of maximal subgroup
• solvable group