quotient group
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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”, in 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”, in Miroslav Hušek, Jan van Mill, editors, Recent Progress in General Topology II, North-Holland: Elsevier, 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.
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
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Further reading
Isomorphism theorems on Wikipedia.Wikipedia - Normal subgroup on Wikipedia.Wikipedia
- List of group theory topics on Wikipedia.Wikipedia
