Characteristic subgroup of finite index

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and subgroup of finite index
View other subgroup property conjunctions | view all subgroup properties

Definition

A characteristic subgroup of finite index is a subgroup of a group that is a characteristic subgroup as well as a subgroup of finite index, i.e., the index of the subgroup is finite, or equivalently, the quotient group is a finite group.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Normal subgroup of finite index
Characteristic core of subgroup of fininte index
Subgroup of finite index Normal subgroup of finite index|FULL LIST, MORE INFO
Characteristic subgroup Characteristic core of subgroup of finite index, Powering-invariant characteristic subgroup, Quotient-powering-invariant characteristic subgroup|FULL LIST, MORE INFO