Characteristic subgroup of finite index
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 | |FULL LIST, MORE INFO | |||
| Characteristic subgroup | |FULL LIST, MORE INFO |