A205645 Number of nilpotent loops of order 2*prime(n) up to isotopism.

3, 64, 3658004, 1023090941561683953759580, 2684673506279593406254437209960379084, 382103603974564085117495134243710834769544696954218618882023686506660

Offset: 2

Author

Jonathan Vos Post, Jan 29 2012

Keywords

• nonn

Comments

Table 5, p. 20, of Clavier. oddprime(n) = A065091(n) = A000040(n-1).

In version 2 of Clavier's preprint as well as in the published paper, the numbers have been replaced by numbers 1 smaller: 2, 63, 3658003... Theorem 6.10, which gives a formula, has also been changed. The arXiv source files include a file with all terms for which prime(n) < 100. That file agrees with this sequence rather than with the sequence in the updated version of the preprint (or in the published paper). - Andrei Zabolotskii, May 06 2025

Examples

			a(4) = 3658004 because prime(4) = 7 and there are 3658004 nilpotent loops of order 2*7 = 14.
		

References

• L. Clavier, About the autotopisms of abelian groups, 2012.
• D. Daly and P. Vojtěchovský, Enumeration of nilpotent loops via cohomology, J. Algebra, 322(11):4080-4098, 2009.
• H.O. Pflugfelder, Quasigroups and Loops: Introduction, 1990.
• J. D. Phillips and P. Vojtěchovský, The varieties of loops of bolmoufang type, Algebra Universalis, 54(3):259-271, 2005.

Links

• Lucien Clavier, Enumeration of nilpotent loops up to isotopy, arXiv:1201.5659v1 [math.GR], Jan 26, 2012.
• Lucien Clavier, Enumeration of nilpotent loops up to isotopy, Commentationes Mathematicae Universitatis Carolinae, 53 (2012), 159-177.

Crossrefs

Cf. A000040, A057771, A065091.