Right Bol Loop 16.3.2.6 of order 16


0123456789101112131415
1250374698131011121514
2571063413101589141112
3014627510131415891211
4306715211129141581310
5762140312118914151013
6437502115141112131098
7645231014151213101189
8913101112151446573021
9131281014111537462150
1089111513141264057312
1110815149121373621405
1214151391181012730564
1312149815101105146273
1415111213109821305746
1511101412813950214637

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.


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:   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