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This tag is for questions relating to "Quotient Group".

A quotient group or factor group is a group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves the group structure.

Definition: If $$G$$ is a group and $$N$$ is a normal subgroup of group $$G$$, then the set $$G/N$$ of all cosets of $$N$$ in $$G$$ is a group with respect to the multiplication of cosets. It is called the quotient group or factor group of $$G$$ by $$N$$. The identity element of the quotient group $$G/N$$ by $$N$$.

• 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.
• The quotient group construction can be viewed as a generalization of modular arithmetic to arbitrary groups. In fact, the quotient group $$G/N$$ is read "$$G$$ mod $$N.$$"
• It can be verified that the set of self-conjugate elements of $$G$$ forms an abelian group $$Z$$ which is called the center of $$G$$.

References:

https://en.wikipedia.org/wiki/Quotient_group

https://brilliant.org/wiki/quotient-group/