Right Bol Loop 16.5.2.8 of order 16


0123456789101112131415
1035247691281015111314
2401673510811139141512
3517062411101314815129
4260715312159814101113
5376104215141291381011
6742530113111415101298
7654321014131512119810
8109121113151475634201
9118101514121367325014
1081213911141554761320
1191581410131241570632
1213101481591136207145
1312141510811910452763
1415131112910802143576
1514119131281023016457

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7   8   14

Middle Nucleus:   0   7

Right Nucleus:   0   7


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

5 Elements of order 2:   1   2   5   6   7

10 Elements of order 4:   3   4   8   9   10   11   12   13   14   15

Commutator Subloop:   0   3   4   7

Associator Subloop:   0   3   4   7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,5)(3,4)(8,12,14,11)(9,15,13,10) is not an automorphism.   L1,1(2*8) neq L1,1(2)*L1,1(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (1024, 4096)


/ revised October, 2001