Group in which every maximal subgroup is characteristic
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
Definition
A group in which every maximal subgroup is characteristic is a group satisfying the following equivalent conditions:
- Any maximal subgroup is a characteristic subgroup.
- Any maximal subgroup is a maximal characteristic subgroup.
Relation with other properties
Stronger properties
Weaker properties
- 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. Further information: Equivalence of definitions of finite nilpotent group