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.