Dictionary

quotient group en · NOUN

Meanings

1. A 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:
   • 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:
   • 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:

Forms

Synonyms

factor group (group obtained from a larger group by aggregating elements)

Translations (3)

it gruppo quoziente (group obtained from a larger group by aggregating elements) · pl grupa ilorazowa (group obtained from a larger group by aggregating elements) · fi tekijäryhmä (group obtained from a larger group by aggregating elements)