How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
Conversely how to show that any semigroup having this property contains a unit and is a group.
Last edited by thomas_donald; Aug 29th 2009 at 05:08 PM.
Thanks a lot!
Can you help me on the first part:
How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
Thanks again!
Thanks a lot!
Can you help me on the first part:
How to prove that in a group, the equations ax=b and ya=b are solvable for any a,b in G.
Thanks again!
That is because $\displaystyle ax=b\Leftrightarrow x=a^{-1}b,ya=b\Leftrightarrow y=ba^{-1}$