Moved - Homomorphism

[kailly]

Anyone could help me with the question stated below

Let f: G - H be a group homomorphism. Show that f is one-to-one if and only if f(e) = {e}

Thank you

 

[daon2]

Anyone could help me with the question stated below

Let f: G - H be a group homomorphism. Show that f is one-to-one if and only if f(e) = {e}

Thank you

You have posted this in News, you should have posted it in Advanced Math.

The question you posted cannot be the right wording (what is {e}?), please check it, and show some effort.

 

[kailly]

Correction of the Question

You have posted this in News, you should have posted it in Advanced Math.

The question you posted cannot be the right wording (what is {e}?), please check it, and show some effort.

Let f: G - H be a group homomorphism. Show that f is one-to-one if and only if f^-1(e) = {e}.

 

[daon2]

Let f: G - H be a group homomorphism. Show that f is one-to-one if and only if f^-1(e) = {e}.

Certainly {e} is a subset of f^(-1)(e); well assuming you know what f^(-1) means and what a homomorphism is.

If x belongs to f^(-1)(e), then f(x)=e. Now what?