# Math Help - Abelian group

1. ## Abelian group

Hi people,

$(G;.)$ is a group.
I must show that if $(\forall a;b \in G): (ab)^2=a^2b^2 \Longrightarrow (G;.)$ is abelian.

Can you help me please???

And thanks.

2. Originally Posted by bhitroofen01
Hi people,

$(G;.)$ is a group.
I must show that if $(\forall a;b \in G): (ab)^2=a^2b^2 \Longrightarrow (G;.)$ is abelian.

Can you help me please???

And thanks.
$ab=ababb^{-1}a^{-1}=(ab)^2b^{-1}a^{-1}=a^2b^2b^{-1}a^{-1}=a^2ba^{-1}$ thus multiplying both sides by $a$ on the left gives $aba=a^2b\implies ba=ab$