quotient group
Noun
Meaning
quotient group (plural quotient groups)
(group theory) A group obtained from a larger group by aggregating elements via an equivalence relation that preserves group structure.
Synonyms
Examples
Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.
Caveats The notation L /K is purely formal and does not imply the formation of a quotient ring or quotient group or any other kind of division.
The quotient group Aut(G) / Inn(G) is usually denoted by Out(G); the non-trivial elements are the cosets that contain the outer automorphisms.
For every positive divisor d of n, the quotient group Z/nZ has precisely one subgroup of order d, the one generated by the residue class of n/d.
Quotient ring main The quotient ring of a ring, is analogous to the notion of a quotient group of a group.
The first isomorphism theorem for groups states that this quotient group is naturally isomorphic to the image of f (which is a subgroup of H).