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. 2001.

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  • 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 — Math. a group, the elements of which are cosets with respect to a normal subgroup of a given group. Also called factor group. [1890 95] * * * …   Universalium

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  • 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

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  • 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

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