Group in which every maximal subgroup is characteristic

Definition
A group in which every maximal subgroup is characteristic is a group satisfying the following equivalent conditions:


 * Any defining ingredient::maximal subgroup is a defining ingredient::characteristic subgroup.
 * Any defining ingredient::maximal subgroup is a defining ingredient::maximal characteristic subgroup.

Stronger properties

 * Weaker than::Cyclic group
 * Weaker than::Group of prime power order in which every maximal subgroup is isomorph-free

Weaker properties

 * Stronger than::Group in which every maximal subgroup is normal
 * Nilpotent group for finite groups, because for a finite group, the group is nilpotent if and only if every maximal subgroup is normal.

Facts

 * Every elementary Abelian p-group occurs as the Frattini quotient of a p-group in which every maximal subgroup is characteristic