# Quotient Group

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## quotient group

[′kwō·shənt ‚grüp]
(mathematics)
A group G / H whose elements are the cosets gH of a given normal subgroup H of a given group G, and the group operation is defined as g1 H · g2 H ≡ (g1· g2) H. Also known as factor group.

## Quotient Group

(or factor group), in mathematics, a group whose elements are the cosets of a given normal subgroup H of a given group G.

References in periodicals archive ?
If N is a normal subgroup of G, the binary operation on left cosets has the structure of a group, the quotient group G/N.
One often has to be able to shift between these two views when thinking about cosets and quotient groups.
The cokernel of [sigma]/l is the quotient group of [[pi].
G, and let U and S be any groups such that U isomorphic with N and S is isomorphic with the quotient group G/N.
G, let U, S be groups such that U is isomorphic with N, and S is isomorphic with the quotient group G/N, that is, there are isomorphisms [upsilon] and [psi] such that;
The group of cosets {H+a: a [member of G} is called the quotient group and is written G/H.
We conclude that Z[subscript n] is not a trivial example of a quotient group, and provide recommendations for teaching Z[subscript n] and other quotient groups.
These three cosets form the so-called quotient group [C.
It introduces group actions early, and includes Hasse diagrams of posets and homomorphism diagrams, while introducing normal subgroups, quotient groups, and homomorphisms late.
He covers set theory, number theory, groups, quotient groups, rings, divisibility in commutative rings, field extensions, group actions, the classification of groups, modules and algebras, Galois theory, multivariable polynomial rings, and categories.
The author has organized the main body of his text in fourteen chapters devoted to sets, relations, and functions, the integers, an introduction to groups, quotient groups and homomorphisms, groups acting on sets, an introduction to rings, and a wide variety of other related subjects.

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