Isomorph-free subgroup of group of prime power order

This article describes a property that arises as the conjunction of a subgroup property: isomorph-free subgroup with a group property imposed on the ambient group: group of prime power order
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Statement

An isomorph-free subgroup of group of prime power order is a subgroup of a group where the group is a group of prime power order and the subgroup is an isomorph-free subgroup.

Relation with other properties

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
characteristic subgroup of group of prime power order	the group is a group of prime power order and the subgroup is a characteristic subgroup	follows from isomorph-free implies characteristic	See prime power order examples in characteristic not implies isomorph-free	|FULL LIST, MORE INFO
normal subgroup of group of prime power order	the group is a group of prime power order and the subgroup is a normal subgroup	Sylow-relatively weakly closed subgroup|FULL LIST, MORE INFO