. . "In mathematics, if G is a group, and H is a subgroup of G, and g is an element of G, thengH = {\u2009gh : h an element of H\u2009} is the left coset of H in G with respect to g, andHg = {\u2009hg : h an element of H\u2009} is the right coset of H in G with respect to g.Only when H is normal will the set of right cosets and the set of left cosets of H coincide, which is one definition of normality of a subgroup."@en . .