On the Solvability of Finite Groups

Abstract

Let M be a subgroup of a finite group G. We define the core of M in G by Cor _G (M) = ∩ _g∈G M ^g . Clearly, Cor _G (M) is the largest normal subgroup of G contained in M. We determine the structure of a finite group G if G possesses a maximal subgroup with core 1 and all maximal subgroups M of G with Cor _G (M) = 1 satisfy a certain property.

Key Words:

• Nilpotent groups
• Solvable groups
• Super solvable groups

2000 Mathematics Subject Classification:

• 20D10
• 20D20
• 20D34

Notes

Communicated by M. R. Dixon.