|
%I #9 Jan 27 2017 05:27:08
%S 0,0,0,0,0,3,0,19,5,16,0,155,0,97,17,6317,0,1901,0,8248,119,10487,0,
%T 471995,119,151971,152701
%N Number of nonassociative right conjugacy closed loops of order n up to isomorphism.
%C 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).
%H G. P. Nagy and P. Vojtechovsky, <a href="http://www.cs.du.edu/~petr/loops">Loops version 3.3.0</a>, Computing with quasigroups and loops in GAP, 2016.
%e 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.
%Y Cf. A090750, A281319, A281462.
%K nonn,more
%O 1,6
%A _Muniru A Asiru_, Jan 24 2017
|
