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Leb

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## Homework Statement

Let [itex]\alpha:G \rightarrow H [/itex] be a homomorphism and let x[itex]\in[/itex]G

Prove [itex]\alpha(<x>) =<\alpha(x)> [/itex]

## Homework Equations

α(<x>) = α({x^{r}: r ∈ Z}) = {α(x^{r}) : r ∈ Z} = {α(x)^{r}: r ∈ Z} = <α(x)>.

I do not understand how can we take out the 'r' out of a(x^{r}) to get (a(x))^{r} ? What would a(x)^2 say mean ? a(x) (some binary operation defined in H) a(x) or would it be (a°a)(x) i.e. a(a(x)) ?