A384190 Number of non-isomorphic AG-groupoids of order n.

1, 3, 20, 331, 31913, 40104513, 643460323187

Offset: 1

Author

Elijah Beregovsky, May 21 2025

Keywords

• nonn
• hard
• more

Comments

A magma S is called an Abel-Grassmann or AG-groupoid (historically they were also called left almost semigroups, right modular groupoids and left invertive groupoids) if for all a,b,c in S (ab)c = (cb)a.

Examples

			For a(2) there are only 3 non-isomorphic AG-groupoids: the null semigroup, the semigroup formed by the set {0,1} under multiplication and the cyclic group Z2.
		

References

• M. A. Kazim and M. Naseerudin, On almost semigroups, Alig. Bull. Math. 2, 1-7 (1972).

Links

• Marek Dančo, Mikoláš Janota, Michael Codish, and João Jorge Araújo, Complete Symmetry Breaking for Finite Models, arXiv:2502.10155 [cs.LO], 2025.
• Marek Dančo, MACE-like model finder for algebraic structures.
• Andreas Distler, Muhammad Shah, and Volker Sorge, Enumeration of AG-Groupoids, Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds) Intelligent Computer Mathematics. CICM 2011. Lecture Notes in Computer Science, vol 6824. Springer, Berlin, Heidelberg.
• Muhammad Iqbal, Imtiaz Ahmad, Muhammad Shah, and Muhammad Irfan Ali, On cyclic associative Abel-Grassman groupoids, arXiv:1510.01316 [math.GR], 2015.
• Index entries for sequences related to groupoids

Crossrefs

Cf. A001329 (magmas), A124506 (semigroups), A001426, A350875, A350874.