quotient group
Jump to navigation
Jump to search
English[edit]
Noun[edit]
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 3manifolds: Papers Dedicated to the Memory of R. H. Fox, Princeton University Press, page 101,
 This paper shows how to compute the quotient groups J^{n}/J^{n+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 N_{H}/T_{H}, and in the present case the Weyl group is simply the permutation group S_{3}.
 2002, Alexander Arhangel'skii, Topological Invariants in Algebraic Environment, Miroslav Hušek, Jan van Mill (editors), Recent Progress in General Topology II, Elsevier (NorthHolland), 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 3manifolds: Papers Dedicated to the Memory of R. H. Fox, Princeton University Press, page 101,
Usage notes[edit]
For a normal subgroup N of G, the quotient group of N in G is denoted G/N (pronounced "G modulo N").
Synonyms[edit]
 (group obtained from a larger group by aggregating elements): factor group
Translations[edit]
group obtained from a larger group by aggregating elements


Further reading[edit]
 Isomorphism theorems on Wikipedia.Wikipedia
 Normal subgroup on Wikipedia.Wikipedia
 List of group theory topics on Wikipedia.Wikipedia