Overview
Given a group {% G %} for which {% H %} is a subset, a coset is a subset of {% G %} that is the result of multiplying an element of {% H %} and an element of {% G %}. There are two different cosets.
Left Coset
{% aH = \{ah | h \in H\} %}
Right Coset
{% Ha = \{ha | h \in H\} %}
Cosets partition {% G %} into disjoint subsets. The number of subsets is called the index of {% H %} in {% G %}, written
{% [G:H] %}