Definition:Coset Space/Left Coset Space

Definition
Let $G$ be a group.

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

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

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

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

Others call it the left coset family.

Others use the term left coset decomposition.

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

Also see

 * Definition:Quotient Group


 * Definition:Right Coset Space