Finite isomorph-free subgroup

This article describes a property that arises as the conjunction of a subgroup property: isomorph-free subgroup with a group property (itself viewed as a subgroup property): finite group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a finite isomorph-free subgroup if it satisfies the following equivalent conditions:

1. It is a finite group and is also an isomorph-free subgroup of the whole group.
2. It is a finite group and is also an isomorph-containing subgroup of the whole group.

Relation with other properties

Stronger properties

• Isomorph-free subgroup of finite group
  • Normal Sylow subgroup
  • Normal Hall subgroup

Weaker properties

• Finite characteristic subgroup
• Finite normal subgroup