Group in which every subgroup is subnormal

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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Definition

A group in which every subgroup is subnormal is a group with the property that every subgroup is a subnormal subgroup.

Relation with other properties

Stronger properties

• Nilpotent group: For proof of the implication, refer Nilpotent implies every subgroup is subnormal and for proof of its strictness (i.e. the reverse implication being false) refer Every subgroup is subnormal not implies nilpotent.

Weaker properties

• Gruenberg group: For proof of the implication, refer Every subgroup is subnormal implies Gruenberg and for proof of its strictness (i.e. the reverse implication being false) refer Gruenberg not implies every subgroup is subnormal.
• Group satisfying normalizer condition: For proof of the implication, refer Every subgroup is subnormal implies normalizer condition and for proof of its strictness (i.e. the reverse implication being false) refer Normalizer condition not implies every subgroup is subnormal.
• Group in which every maximal subgroup is normal