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What (who) is Quotient group - definition
Quotient group
![The cosets of the fourth [[roots of unity]] ''N'' in the twelfth roots of unity ''G''.](https://commons.wikimedia.org/wiki/Special:FilePath/Normal subgroup illustration.svg?width=200 "The cosets of the fourth [[roots of unity]] ''N'' in the twelfth roots of unity ''G''.")
GROUP OBTAINED BY AGGREGATING SIMILAR ELEMENTS OF A LARGER GROUP
Quotient (group theory); Quotient groups; Factor group
A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo n can be obtained from the group of integers under addition by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class (known as a congruence class) as a single entity.
Quotient space (linear algebra)
VECTOR SPACE CONSISTING OF AFFINE SUBSETS
Linear quotient space; Quotient vector space
In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by "collapsing" N to zero. The space obtained is called a quotient space and is denoted V/N (read "V mod N" or "V by N").
Ideal quotient
BINARY OPERATION DEFINED ON THE SET OF IDEALS IN A COMMUTATIVE RING; (I:J) CONSISTS OF ELEMENTS R OF THE COMMUTATIVE RING SUCH THAT RJ IS A SUBSET OF I; IN ALGEBRAIC GEOMETRY, CORRESPONDS TO THE SET DIFFERENCE OF SUBVARIETIES
Quotient ideal; Colon ideal
In abstract algebra, if I and J are ideals of a commutative ring R, their ideal quotient (I : J) is the set
