Erratum in A First Course in Abstract Algebra for isomorphism

Question

I don't really know where to post this but, I think I found an erratum in John Fraleigh's book: "A First Course in Abstract Algebra". On page 29, Definition 3.7, Fraleigh defines an isomorphism in such terms:

Let $\langle S, \star \rangle$ and $\langle S^{'}, \star^{'} \rangle$ be binary algebraic structures. An isomorphism of $S$ with $S^{'}$ is a one-to-one function $\phi$ mapping $S$ onto $S^{'}$ such that: $\phi(x \star y) = \phi(y) \star^{'} \phi(y)$ for all $x, y \in S$

Now, I've looked here at the list of errata for the 7th edition and while there is one on page 29, it doesn't relate to the definition. However, surely the definition is meant to say $\phi(x) \star^{'} \phi(y)$ instead of $\phi(y) \star^{'} \phi(y)$ right?

Answer 1

Does anyone know of an errata sheet for the 8th edition? On page 53, in the section on subgroups, Theorem 5.15 reads: "A nonempty subset $H$ of the group $G$ is a subgroup of $G$ if and only if for all $a,b \in G$, $ab^{-1}\in G$", but I think this should read "A nonempty subset $H$ of the group $G$ is a subgroup of $G$ if and only if for all $a,b \in H$, $ab^{-1}\in H$", as this was problem 45 in the 7th edition.