1
$\begingroup$

let $(B,\star)$ defines a monoid with a finite number of elements Let. the elements of $B$ be $\{x_1,x_2,x_3,x_4,\cdots\}$ where every element of $B$ occurs exactly once in this list

let $y$ be the invertible element of the monoid.

Prove that every element of the monoid occurs exactly once in this list $\{ y\star x_1,y \star x_2, \cdots, y\star x_n \}$.

Can anyone please point me in the right direction where to start? without telling me the answer.

$\endgroup$
  • 1
    $\begingroup$ Start by trying to clearly and precisely state the problem. $\endgroup$ – user14972 Dec 27 '12 at 2:15
  • 1
    $\begingroup$ What do you mean it 'occurs exactly once'? $\endgroup$ – Alexander Gruber Dec 27 '12 at 2:17
  • $\begingroup$ @AlexanderGruber I have edited the question.Can you please advise me. $\endgroup$ – Jack welch Dec 27 '12 at 2:22
  • $\begingroup$ Hint: suppose that $y*x_i = y*x_j$, and show that $i$ must equal $j$. So the map $x_k \mapsto y*x_k$ is injective. $\endgroup$ – Josh Keneda Dec 27 '12 at 2:25
2
$\begingroup$

If $yx_i=yx_j$, what can you determine about $x_i$ and $x_j$, knowing that $y$ is invertible?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.