[GAP Forum] semigroup of some order

[Jean-Eric Pin]

Dear Jalal Molavi,

To my knowledge, only the number of non-isomorphic commutative 
semigroups of order <= 10 is known. See

Pierre Antoine Grillet, Computing Finite Commutative Semigroups: Part II
Semigroup Forum 67, Number 2, 2003, 159-184 (and Part III, 185-204)

For general semigroups, the larger known order seems to be 8

Semigroups of order 8, S. Satoh, K. Yama, and M. Tokizawa. Semigroup 
Forum 49, 1994, pages 7-29.

Best regards,

Jean-Eric Pin


At 12:59 +0000 2/03/05, jalal molavi wrote:
>Dear gap- forum.
>I have a question .
>Is there any classification about semigroup such as group.
>in the other hand how many semigroups are there of size n
>where n is natural number.
>i need all semigroups of size less than 10.
>if any one have usefull information i am very thankful to know that.
>Best regards.