Right Bol Loop 16.3.2.97 of order 16


0123456789101112131415
1036725491512131011814
2341670510128914151113
3274501611101415891312
4765032115141312111098
5610347212139815141011
6507214313111514981210
7452163014811101312159
8910111512131441635270
9811131410121574362501
1011159131481265417032
1110141512891352140763
1213981115141036704125
1312814109151123071456
1415121091311810526347
1514131281110907253614

Centre:   0   4

Centrum:   0   4

Nucleus:   0   4

Left Nucleus:   0   3   4   5

Middle Nucleus:   0   4

Right Nucleus:   0   4


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:   1   4   7

12 Elements of order 4:   2   3   5   6   8   9   10   11   12   13   14   15

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-1

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

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

Right (Left, Full) Mult Group Orders:   64 (128, 512)


/ revised October, 2001