A281554 Number of nonassociative right conjugacy closed loops of order n up to isomorphism.

0, 0, 0, 0, 0, 3, 0, 19, 5, 16, 0, 155, 0, 97, 17, 6317, 0, 1901, 0, 8248, 119, 10487, 0, 471995, 119, 151971, 152701

Offset

1,6

Comments

For a groupoid Q and x in Q, define the right (left) translation map R_x: Q->Q by yR_x=yx (L_x: Q->Q by yL_x=xy). A loop is a groupoid Q with neutral element 1 in which all translations are bijections in Q. A loop Q is right conjugacy closed if (R_x)^(-1)R_yR_x is a right translation for every x, y in Q. Since any finite loop of order n < 5 is a group, then nonassociative right conjugacy closed loops exist when the order n > 5. In the literature, every nonassociative right conjugacy closed loop of order n can be represented as a union of certain conjugacy classes of a transitive group of degree n. The number of nonassociative right conjugacy closed loops of order n up to isomorphism were summarized in LOOPS version 3.3.0, Computing with quasigroups and loops in GAP (Groups, Algorithm and Programming).

Links

Table of n, a(n) for n=1..27.

G. P. Nagy and P. Vojtechovsky, Loops version 3.3.0, Computing with quasigroups and loops in GAP, 2016.

Example

a(6)=3 because there are 3 nonassociative right conjugacy closed loops of order 6 and a(8)=19 because there are 19 nonassociative right conjugacy closed loops of order 8.

Crossrefs

Cf. A090750, A281319, A281462.

Sequence in context: A013579 A151814 A187804 * A320104 A102840 A009353

Adjacent sequences: A281551 A281552 A281553 * A281555 A281556 A281557

Keyword

nonn,more

Author

Muniru A Asiru, Jan 24 2017

Status

approved