Quotient loop

Definition

Suppose $(L,*)$ is an algebra loop and $N$ is a normal subloop of $L$. The quotient loop $L/N$ is defined as the following algebra loop:

1. The set of elements of $L/N$ is the set of left cosets of $N$, i.e., subsets of the form $a * N$, with $a \in L$.
2. The multiplication is defined by $(a * N) * (b * N) = (a * b) * N$. That this is well-defined follows from the definition of normal subloop.