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Keywords:
loop; nilpotent; enumeration; cohomology; isomorphy; isotopy
loop; nilpotent; enumeration; cohomology; isomorphy; isotopy
Summary:
We modify tools introduced in [Daly D., Vojtěchovský P., Enumeration of nilpotent loops via cohomology, J. Algebra 322 (2009), no. 11, 4080--4098] to count, for any odd prime $q$, the number of nilpotent loops of order $2q$ up to isotopy, instead of isomorphy.
References:
[Cla12] Clavier L.: About the autotopisms of abelian groups. 2012, http://arxiv.org/abs/1201.5655
[DV09] Daly D., Vojtěchovský P.: Enumeration of nilpotent loops via cohomology. J. Algebra 322 (2009), no. 11, 4080–4098. DOI 10.1016/j.jalgebra.2009.03.042 | MR 2556139 | Zbl 1209.20068
[Pfl90] Pflugfelder H.O.: Quasigroups and Loops: Introduction. Heldermann, Berlin, 1990. MR 1125767 | Zbl 0715.20043
[PV05] Phillips J.D., Vojtěchovský P.: The varieties of loops of Bol-Moufang type. Algebra Universalis 54 (2005), no. 3, 259–271. DOI 10.1007/s00012-005-1941-1 | MR 2219409 | Zbl 1102.20054
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