The function $f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian. Can anyone give me any tips how to work on this question?
Asked
Active
Viewed 2,459 times
4
-
4What have you tried? There is not really any trick involved here, just the definitions. – Tobias Kildetoft May 29 '13 at 01:49
-
oh i see! just accept it. Thanks! – megan May 29 '13 at 02:01
-
@Megan, you still don't accept the Peter's answer (and any answer of your other questions) If you don't know how accept an answer you sould see http://math.stackexchange.com/faq#howtoask – Gaston Burrull May 29 '13 at 03:10
1 Answers
4
Hint When is it true that $(ax)^2=a^2x^2$? That is $$axax=aaxx$$
Further hint Multiplying on the left by $a^{-1}$ and right by $x^{-1}$ gives what?
Pedro
- 122,002
-
3oh i see! like homomorphism theory:f(ab)=f(a)f(b), when f(x)=x^2. f(a)=a^2, f(b)=b^2,f(ab)=(ab)^2=a^2b^2. f(ab)=f(a)f(b)! right? – megan May 29 '13 at 01:54
-