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I am working the problems in Lang's Algebra. I am on number 12(c) on Chapter 1 [revised third edition], it states

let H and N be groups and let f: H --> Aut(N) be given homomorphism Define G = NxH with the law

(a,b)(a',b') = (a'f(b)a',bb').

the problem is that f(b) is a member of Aut(N) and so the definition is ambiguous at best. I mean I suppose it could mean f(b) applied to a' (or even applied a). But this doesn't fit the notation of the rest of the book. Any comments on this?

let H and N be groups and let f: H --> Aut(N) be given homomorphism Define G = NxH with the law

(a,b)(a',b') = (a'f(b)a',bb').

the problem is that f(b) is a member of Aut(N) and so the definition is ambiguous at best. I mean I suppose it could mean f(b) applied to a' (or even applied a). But this doesn't fit the notation of the rest of the book. Any comments on this?

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