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

‎The Theorem ۱۲ in [A note on‎ ‎p-nilpotence and solvability of finite groups‎, ‎J‎. ‎Algebra ۳۲۱‎ ‎(۲۰۰۹) ۱۵۵۵--۱۵۶۰.] 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.

کلیدواژه ها:

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