Subgroup (Noun)
Meaning 1
(mathematics) a subset (that is not empty) of a mathematical group.
Classification
Nouns denoting cognitive processes and contents.
Examples
- The symmetries of the cube form a subgroup of the group of rotations of 3D space.
- A normal subgroup is a subgroup that is invariant under conjugation by any element of the group.
- Every subset of a finite group generates a cyclic subgroup, unless it contains only the identity.
- A subset H of G is a subgroup of G if it contains the identity, and if the inverse and the product of any two of its elements are in H.
- A one-element subset containing the identity element forms the smallest subgroup, often referred to as the trivial subgroup.
Hypernyms
Meaning 2
A distinct and often subordinate group within a group.
Classification
Nouns denoting groupings of people or objects.