Howson property

In the mathematical subject of group theory, the Howson property, also known as the finitely generated intersection property (FGIP), is the property of a group saying that the intersection of any two finitely generated subgroups of this group is again finitely generated. The property is named after Albert G. Howson who in a 1954 paper established that free groups have this property.
Formal definition.
A group formula_1 is said to have the Howson property if for every finitely generated subgroups formula_2 of formula_1 their intersection formula_4 is again a finitely generated subgroup of formula_1.