Right Bol Loop 16.3.2.5 of order 16


0123456789101112131415
1250374691411101312158
2571063413101589141112
3014627510118151491213
4306715211129141581310
5762140312131498151011
6437502115813121110914
7645231014151213101189
8151312111091421305746
9111214108131557412630
1014913151181214037562
1112891415101305146273
1281511913141062750314
1310141589121173621405
1491110131215846573021
1513108121411930264157

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   10   12

4 Elements of order 4:   2   4   9   15

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:   HOLDS

Al Property:   FAILS. The left inner mapping L1,1 = (8,13)(9,10)(11,14)(12,15) 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