Isomorph-free maximal subgroup of finite group

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

Definition

An isomorph-free maximal subgroup of finite group is a subgroup of a finite group satisfying the following equivalent conditions:

1. It is both an isomorph-free subgroup (in particular, isomorph-free subgroup of finite group)and a maximal subgroup (in particular, a maximal subgroup of finite group) of the whole group.
2. It is both an isomorph-containing subgroup and a maximal subgroup of the whole group.
3. It is both a prehomomorph-contained subgroup and a maximal subgroup of the whole group.

Relation with other properties

Stronger properties

• Isomorph-free maximal subgroup of group of prime power order

Weaker properties

• Maximal subgroup of finite group
• Isomorph-free subgroup of finite group