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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Inverses in finite monoids ...
Replies: 1   Last Post: Nov 21, 2011 6:14 AM

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riderofgiraffes

Posts: 408
From: UK
Registered: 1/11/07
Inverses in finite monoids ...
Posted: Nov 18, 2011 5:57 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I posted this question the other day but it got no
responses and I was wondering if perhaps no one saw
it, or if it's uninteresting because it's not an
argument about whether infinity exists.

It's strictly a finite question. Really hoping someone
can suggest a line of attack.

If element "a" has a right inverse in a finite monoid,
does it necessarily follow that it has a left inverse?
I know that there are natural numbers m and n with m<n
and a^m=a^n, and I know that if the left inverse exists
then it's equal to the right inverse (and unique).

But I'm stuck on existence.

Suggestions welcome - thanks

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