(linear algebra, group theory) For given field F and positive integer n, the group of 2n×2n symplectic matrices with elements in F.

plural of symplectic group

plural of group therapy

(category theory) Given a category C, any object X ∈ C on which morphisms are defined corresponding to the group theoretic concepts of a binary operation (called multiplication), identity and inverse, such that multiplication is associative and properties are satisfied that correspond to the existence of inverse elements and the identity element.

plural of group object

plural of group scheme

(category theory, scheme theory) A group object that is an object in a category of schemes; a scheme that has certain properties that generalise the concept of group.

plural of group functor

(category theory, algebraic geometry) A group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group.

(economics, sociology) A group in a given population having an income within a specified range.