# Ambiguous Group Law

1. Jun 10, 2008

### eastside00_99

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?

Last edited: Jun 10, 2008
2. Jun 10, 2008

### morphism

(Should that be "(a f(b) a', bb')" instead?)

I'm pretty sure it's supposed to mean f(b) applied to a'. It looks like the exercise is attempting to walk you through the construction of the semidirect product of two groups.

3. Jun 10, 2008

### eastside00_99

yeah i meant a instead of a' up there. Ok, I guess that has to be what it is then. Thanks.