quotient divisible group - перевод на русский
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quotient divisible group - перевод на русский

GROUP OBTAINED BY AGGREGATING SIMILAR ELEMENTS OF A LARGER GROUP
Quotient (group theory); Quotient groups; Factor group
  • The cosets of the fourth [[roots of unity]] ''N'' in the twelfth roots of unity ''G''.

quotient divisible group      
делимая фактор-группа
factor group         

общая лексика

факторгруппа

quotient group         

общая лексика

факторгруппа

Определение

Крайслер

Википедия

Quotient 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 {\displaystyle n} and defining a group structure that operates on each such class (known as a congruence class) as a single entity. It is part of the mathematical field known as group theory.

For a congruence relation on a group, the equivalence class of the identity element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting quotient is written G / N {\displaystyle G\,/\,N} , where G {\displaystyle G} is the original group and N {\displaystyle N} is the normal subgroup. (This is pronounced G mod N {\displaystyle G{\bmod {N}}} , where mod {\displaystyle {\mbox{mod}}} is short for modulo.)

Much of the importance of quotient groups is derived from their relation to homomorphisms. The first isomorphism theorem states that the image of any group G under a homomorphism is always isomorphic to a quotient of G {\displaystyle G} . Specifically, the image of G {\displaystyle G} under a homomorphism φ : G H {\displaystyle \varphi :G\rightarrow H} is isomorphic to G / ker ( φ ) {\displaystyle G\,/\,\ker(\varphi )} where ker ( φ ) {\displaystyle \ker(\varphi )} denotes the kernel of φ {\displaystyle \varphi } .

The dual notion of a quotient group is a subgroup, these being the two primary ways of forming a smaller group from a larger one. Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup. In category theory, quotient groups are examples of quotient objects, which are dual to subobjects.

Как переводится quotient divisible group на Русский язык