Dear Joao,
If the question is: Let S and T be semigroups of transformations of
degree n where |S|=10 and |T|=11. Then is S a subsemigroup of T?
Then the answer is yes, just use ForAll(S, x-> x in T);
If the question is: Let S be a semigroup of transformations where |S|
=10. Then does there exist T such that |T|=11 and S embeds in T?
Then the answer is no, there is no method installed in GAP to handle
this situation.
If the question is: Let S be a semigroup of degree 10 given by its
Cayley table and let T be a semigroup of degree 11 given by its
Cayley table. Then is S isomorphic to a subsemigroup of T?
Then the answer is: it is possible to do this in GAP but the method
is not efficient. Look at the orbits of the 11 10x10 subtables of the
Cayley table of T inside the symmetric group on 11 points acting on
the pairs (i,j) i, j in {1,...,11}. If the Cayley table for S lies in
any of these orbits, then the answer is yes! Otherwise, the answer is
no. However it might take a long time to tell you an answer.
Let me know if that helps.
Regards,
James
Message: 6
Date: Fri, 15 Jun 2007 14:47:32 +0100 (WEST)
From: Joao Araujo <[EMAIL PROTECTED]>
Subject: [GAP Forum] test for subsemigroups
To: [EMAIL PROTECTED]
Message-ID: <[EMAIL PROTECTED]>
Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
Dear Forum,
I would be grateful if someone could tell me if there is in GAP an
easy way to check if a 10-elements semigroup of transformations S
can be embedded in an 11-elements semigroup of transformations T.
I thank in advance,
Joao
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