Abstract Algebra/Group Theory/Subgroup/Coset/Definition of a Coset

Let g be a fixed element of Group G. Let H be a subgroup of G.

h*g is in right coset Hg if h is in subgroup H of G and g is in group G.

Left Coset of H by g is gH.

Right Coset of H by g is Hg.

Notice that such cosets are not necessarily subgroups of G.