What are the cosets of this presentation? I'm reading a book on algebra, and they give a presentation for $S_3$, with 6 elements $\{1, x, x^2, y, x y, x^2y\}$ as $$x^3 = 1,\quad y^2 = 1,\quad y x=x^2y$$
Now later in the book, there is a subgroup $H = \{1, x y\}$.  So they give the left cosets of $H$ in this group as
$$\{1, x y\} = H = xyH$$
$$\{x, x^2 y\} = xH = x^2yH$$
$$\{x^2 y\} = x^2H = yH$$
The last set of equations is what concerns me.  I think it should be 
$$\{x^2, y\} = x^2H = yH$$  Am I correct?  If not, what am I missing?

As confirmed by Tyler in the comments, you are correct. What appears in the book is missing a comma.
