quotient group
English
Noun
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.
- 1975, John R. Stallings, Quotients of the Powers of the Augmentation Ideal in a Group Ring, Lee Paul Neuwirth (editor), Knots, Groups, and 3-manifolds: Papers Dedicated to the Memory of R. H. Fox, Princeton University Press, page 101,
- 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).
- 1983, David H. Sattinger, Branching in the Presence of Symmetry, Society for Industrial and Applied Mathematics, page 33,
- The Weyl group is the quotient group NH/TH, and in the present case the Weyl group is simply the permutation group S3.
- 2002, Alexander Arhangel'skii, Topological Invariants in Algebraic Environment, Miroslav Hušek, Jan van Mill (editors), Recent Progress in General Topology II, Elsevier (North-Holland), page 39,
- 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.
- 1975, John R. Stallings, Quotients of the Powers of the Augmentation Ideal in a Group Ring, Lee Paul Neuwirth (editor), Knots, Groups, and 3-manifolds: Papers Dedicated to the Memory of R. H. Fox, Princeton University Press, page 101,
Usage notes
For a normal subgroup N of G, the quotient group of N in G is denoted G/N (pronounced "G modulo N").
Synonyms
- (group obtained from a larger group by aggregating elements): factor group
Translations
group obtained from a larger group by aggregating elements
|
|
Further reading
This article is issued from
Wiktionary.
The text is licensed under Creative
Commons - Attribution - Sharealike.
Additional terms may apply for the media files.