A281462 Number of code loops of order n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0

Offset

1,16

Comments

A code loop is a Moufang 2-loop Q with a central subloop Z of order 2 such that Q/Z is an elementary abelian group. The library named code in LOOPS version 2.2.0, Computing with quasigroups and loops in GAP (Groups, Algorithm and Programming), contains all nonassociative code loops of order less than 65. Every code loop is a Moufang loop but not conversely. The GAP command IsCodeLoop(MoufangLoop(n,m)) gives the m-th nonassociative code loop of order n in the LOOPS Package library. Code loops of small orders were classified by G. P. Nagy and P. Vojtechovsky.

(Groups are specifically excluded from the counts.)

Links

Table of n, a(n) for n=1..65.

R. L. Griess Jr.,  Code loops, J. Algebra 100(1986), 224-234.

G. P. Nagy and P. Vojtechovsky, The Moufang loops of order 64 and 81, Symbolic Comput., 42(2007), 871-883.

G. P. Nagy and P. Vojtechovsky, Loops version 2.2.0, Computing with quasigroups and loops in GAP, 2012.

Example

a(16)=5 because all the 5 Moufang loops of order 16 are code loops;
a(32)=16 because only 16 of the 71 Moufang loops of order 32 are code loops.

Crossrefs

Cf. A090750, A281319.

Sequence in context: A152623 A020761 A341881 * A236239 A047752 A088194

Adjacent sequences: A281459 A281460 A281461 * A281463 A281464 A281465

Keyword

nonn

Author

Muniru A Asiru, Jan 22 2017

Status

approved