Double coset index of a subgroup

Definition

Symbol-free definition

The double coset index of a subgroup in a group is the cardinality of its double coset space, or equivalently, the number of double cosets the subgroup has.

Related properties

Related subgroup properties

• Subgroup of double coset index two

Facts

• Double coset index two implies maximal
• Bound on double coset index in terms of orders of group and subgroup
• Index three implies normal or double coset index two
• Index four implies 2-subnormal or double coset index two