University of Isfahan International Journal of Group Theory 2251-7650 6 2 2017 06 01 A note on finite groups with the indices of some maximal subgroups being primes 17 20 12396 10.22108/ijgt.2017.12396 EN Cui Zhang Yantai University Journal Article 2015 08 07 ‎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. Non-abelian simple group the index of maximal subgroup solvable group https://ijgt.ui.ac.ir/article_12396_c6588acf55ed792ee5a449031ab6b69a.pdf