Finite double coset index is not finite-intersection-closed
This article gives the statement, and possibly proof, of a subgroup property (i.e., subgroup of finite double coset index) not satisfying a subgroup metaproperty (i.e., finite-intersection-closed subgroup property).
View all subgroup metaproperty dissatisfactions | View all subgroup metaproperty satisfactions|Get help on looking up metaproperty (dis)satisfactions for subgroup properties
Get more facts about subgroup of finite double coset index|Get more facts about finite-intersection-closed subgroup property|
An intersection of finitely many subgroups, each having finite double coset index in the whole group, need not have finite double coset index in the whole group.
More specifically, it is possible to have two subgroups , both with finite double coset index in , such that does not have finite double coset index in .