Subgroup of index two
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Definition with symbols
A subgroup of a group is said to be of index two if .
This subgroup property is a first-order subgroup property, viz., it has a first-order description in the theory of groups.
View a complete list of first-order subgroup properties
The property of being a subgroup of index two can be expressed in first-order logic (in fact, the property of being a subgroup of any fixed finite index can be expressed in first-order logic).
Relation with other properties
- Normal subgroup: For full proof, refer: index two implies normal
- Subgroup of prime index
- Abelian-quotient subgroup