quotient group

plural quotient groups

1. group theoryA group obtained from a larger group by aggregating elements via an equivalence relation that preserves group structure.

   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

   2 more examples

   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. Fox, Princeton University Press, page 101

   The class of reflexive groups doesn't behave nicely with regards to operations: a closed subgroup of a reflexive group need not be reflexive, and a quotient group of a reflexive group need not be reflexive.

   2002, Alexander Arhangel'skii, “Topological Invariants in Algebraic Environment”, in Miroslav Hušek, Jan van Mill, editors, Recent Progress in General Topology II, North-Holland: Elsevier, page 39

   Synonyms: factor group