Group in which every maximal subgroup is normal
From Groupprops
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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This is a variation of nilpotence|Find other variations of nilpotence | Read a survey article on varying nilpotence
Definition
A group in which every maximal subgroup is normal is a group satisfying the following equivalent conditions:
- Any maximal subgroup (i.e. any proper subgroup not contained in any other proper subgroup) is a normal subgroup
- Any maximal subgroup is a maximal normal subgroup
- There does not exist any maximal subgroup that is contranormal
- There does not exist any maximal subgroup that is self-normalizing