For problem number 5b it reads:

The product of the permutations of and of (in one-line notation) is the permutation of .

Should this instead read as follows:

The product of the permutations of and of (in one-line notation) is the permutation of .

So should the addition of the on the elements be a subscript?

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I do not think it is a typo.

Consider the following example: Take the sets and and consider the permutations and –both in one-line notation.

Then the product of the above two permutations would be , which is indeed a permutation of If we take your suggestion, I don’t see how the multiplication would make sense because we don’t have .

I was wondering about the same thing…We don’t usually put commas in the one line notation, do we? Like in the example in the footnote.

The problem is correct as stated. As for commas in one-line notation, they are necessary if the terms are more complicated than just one-digit numbers or single variables, as in this case. Without commas, the permutation would be an unreadable mess: .