# Erratum in A First Course in Abstract Algebra for isomorphism

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?

• Yep, it's a definite typo. Also note that there is a second unofficial errata sheet. Commented Mar 2, 2019 at 21:01
• Yes, I think so (b.t.w. errata is a plural – singular is erratum). Commented Mar 2, 2019 at 21:02
• Cool thanks! Funny how this one is also not present on the unofficial one. I would have presumed that definition, being a very important part of mathematics, would be check twice. Commented Mar 2, 2019 at 21:02
• @DatCorno Typos are hard to avoid sometimes. And you have a typo yourself:"would be check twice". Commented Mar 2, 2019 at 21:21
• I'm voting to close this question as off-topic because it's an obvious typo so adds no value to the site. Commented Mar 3, 2019 at 21:05

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.