Right Bol Loop 16.3.2.4 of order 16

0123456789101112131415
1250374698131011121514
2571063413101589141112
3014627510131415891211
4306715211129141581310
5762140312118914151013
6437502115141112131098
7645231014151213101189
8151312111091421305746
9111214108131550214637
1014913151181212730564
1112891415101305146273
1281511913141064057312
1310141589121173621405
1491110131215846573021
1513108121411937462150

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7

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

3 Elements of order 2:   7   9   15

4 Elements of order 4:   2   4   10   12

8 Elements of order 8:   1   3   5   6   8   11   13   14

Commutator Subloop:   0   2   4   7

Associator Subloop:   0   2   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)(9-1) neq (1*9)-1

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

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

Right (Left, Full) Mult Group Orders:   64 (4096, 16384)

/ revised October, 2001