 quotient group

Math.a group, the elements of which are cosets with respect to a normal subgroup of a given group. Also called factor group.[189095]
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Universalium. 2010.
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Universalium. 2010.
Quotient group — In mathematics, given a group G and a normal subgroup N of G , the quotient group, or factor group, of G over N is intuitively a group that collapses the normal subgroup N to the identity element. The quotient group is written G / N and is… … Wikipedia
quotient group — noun : a group whose elements are the cosets of a normal subgroup of a given group called also factor group * * * Math. a group, the elements of which are cosets with respect to a normal subgroup of a given group. Also called factor group. [1890… … Useful english dictionary
quotient group — noun Date: 1893 a group whose elements are the cosets of a normal subgroup of a given group called also factor group … New Collegiate Dictionary
quotient group — The group G/N whose elements are the cosets of N in G, where N is a normal subgroup of G. The product of two cosets is defined to be equal to the coset which contains the product of an element of the first coset and an element of the second … Dictionary of automotive terms
Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… … Wikipedia
Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines … Wikipedia
Quotient ring — In mathematics a quotient ring, also known as factor ring or residue class ring, is a construction in ring theory, quite similar to the factor groups of group theory and the quotient spaces of linear algebra. One starts with a ring R and a two… … Wikipedia
Quotient space — In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or gluing together certain points of a given space. The points to be identified are specified … Wikipedia
Quotient category — In mathematics, a quotient category is a category obtained from another one by identifying sets of morphisms. The notion is similar to that of a quotient group or quotient space, but in the categorical setting.DefinitionLet C be a category. A… … Wikipedia
Group extension — In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence:1 ightarrow N… … Wikipedia