Definition:Coset Space/Right Coset Space

Definition
Let $G$ be a group.

Let $H$ be a subgroup of $G$.

The right coset space (of $G$ modulo $H$) is the quotient set of $G$ by right congruence modulo $H$, denoted $G / H^r$.

It is the set of all the right cosets of $H$ in $G$.

Also known as
Some sources call this the right quotient set.

Others call it the right coset family.

Others use the term right coset decomposition.

Some sources use a hyphen: right-coset space or right-coset family, and so on.

Also see

 * Definition:Left Coset Space