Outrageously Funny Word Dictionary :: Subgroup

👉 A group composed of two or more distinct elements, often denoted by symbols like \( \langle X, \sim \rangle \) or \( C(n, k) \), where \( n \) is a positive integer and \( k > 1 \). In this context, a subgroup is a subset of the group that is closed under certain operations.

Subgroup

👉 In mathematics, a subgroup is a subset of a group that is closed under the group operation and has an identity element. It consists of elements that are also in the original group (i.e., they have inverses). The set of all subgroups of a given group forms a group itself called the quotient group or factor group.

subgroups

👉 In mathematics, a subgroup is a subset of a group that is closed under the group operation and contains the identity element. A subgroup can be defined as any subset of a given group that includes all of its elements and has an identity element (the unique element in the group that when multiplied by another element gives back the original element). Subgroups are fundamental to many parts of mathematics, including group theory and abstract algebra.

subgroup