Fully invariant subgroup of group of prime power order

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

A subgroup of a group is termed a fully invariant subgroup of group of prime power order if the whole group is a group of prime power order (i.e., a finite $p$-group for some prime number $p$) and the subgroup is a fully invariant subgroup.

Relation with other properties

Stronger properties

• Verbal subgroup of group of prime power order

Weaker properties

• Characteristic subgroup of group of prime power order
• Finite-p-potentially verbal subgroup
• Finite-p-potentially characteristic subgroup
• Normal subgroup of group of prime power order