Subgroup of finite group

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This article describes a property that arises as the conjunction of a subgroup property: 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

A subgroup of finite group is a subgroup inside a finite group.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite subgroup subgroup that is finite, i.e., its order is a finite number
Subgroup of finite index subgroup whose index is a finite number