Are finite semi groups which obey cancellation law abelian groups?

Asked Oct 03 '20 at 12:14

Active Oct 03 '20 at 12:33

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I've found this problem in an exercise. I've searched it in the web but I've found one which says that it is a group but, in my version of the problem it's says that: "show that finite semi groups which obey cancellation law are abelian groups".

Is there a mistake in this problem?

edited Oct 03 '20 at 12:33

J.-E. Pin

42,871

asked Oct 03 '20 at 12:14

Abdullah O. Alfaqir

Is there a mistake in what problem? The answer to the question in the title is no. – Derek Holt Oct 03 '20 at 12:22
„says it is a group“ and „in my version [...] are groups“ don’t really contradict... Where does the abelian in the title come from? – Jonas Linssen Oct 03 '20 at 12:25
1

Obviously every finite group is a finite semigroup with cancellation, let it be Abelian or not. – Berci Oct 03 '20 at 12:25
@PrudiiArca that's my question – Abdullah O. Alfaqir Oct 03 '20 at 12:28
See this question. – J.-E. Pin Oct 03 '20 at 12:32
@DerekHolt thanks – Abdullah O. Alfaqir Oct 03 '20 at 12:33
@DerekHolt yes I've forgotten to write it as in the title between quotation marks_more specifically I forgot to mention abelian – Abdullah O. Alfaqir Oct 03 '20 at 12:35

Are finite semi groups which obey cancellation law abelian groups?

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