quotient group

Noun

quotient group (plural quotient groups)

1. A group obtained from a larger group by aggregating elements via an equivalence relation that preserves group structure.
   • This paper shows how to compute the quotient groups Jⁿ/Jⁿ⁺¹ (as well as the multiplicative structure of the graded ring consisting of these quotient groups).1975, John R. Stallings, “Quotients of the Powers of the Augmentation Ideal in a Group Ring”, in Lee Paul Neuwirth, editor, Knots, Groups, and 3-manifolds: Papers Dedicated to the Memory of R. H....
   • The Weyl group is the quotient group N_H/T_H, and in the present case the Weyl group is simply the permutation group S₃.1983, David H. Sattinger, Branching in the Presence of Symmetry, Society for Industrial and Applied Mathematics, page 33

   Synonyms:

   factor group