Can someone help me with this...TIA
Let G be a group which satisfies the following property:
Whenever x,y,z are elements of G such that xy=yz, then x=z.
Prove that G must be Abelian.
I don't even know how to start. TIA...
I have NO experience with Abstract Algebra whatsoever, but for some reason i felt like taking a stab at this.
According to Wikipedia, an Abelian group is a group (G,*) such that a*b = b*a for all a,b in G.
now we are told that $\displaystyle xy = yz \implies x = z$, for any $\displaystyle x,y,z$ in G
this means that we can write, $\displaystyle xy = yx$ or alternatively, $\displaystyle zy = yz$. Which is the exact definition of an Abelian Group.
don't take my word for it though, wait until the experts get here