I found a paper, but here the author solves a bit different problem. My question is: Is there any efficient algorithm for computing all semigroups of order n?
2026-03-27 19:40:28.1774640428
Is there any efficient algorithm for computing all semigroups of order n?
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There is no efficient algorithm for computing all the semigroups of order $n$. The number of semigroups of order 10 is not even known (up to isomorphism and anti isomorphism). This is an extremely hard problem, and the number of semigroups grows very very quickly.
Almost all semigroups of any given size are 3-nilpotent, meaning that the product of any three elements is some fixed element 0, and that there is a product of two elements that is not 0. Arguably these semigroups are not very interesting.
See my answer here where I answer a similar question.
A library of all semigroups with order at most 8 (again up to isomorphism and anti isomorphism) is available in the GAP package Smallsemi.