Right Bol Loop 16.7.4.4 of order 16


0123456789101112131415
1032674598111013121514
2301765410118914151213
3210547611109815141312
4675031213121514981110
5764302114151213101189
6457120312131415891011
7546213015141312111098
8912101114131510324675
9813111015121401236457
1011148912151332107546
1110159813141223015764
1213814151091146751032
1312915141181064570123
1415101213811975463210
1514111312910857642301

Centre:   0   7

Centrum:   0   1   5   7

Nucleus:   0   7

Left Nucleus:   0   1   2   3   4   5   6   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

7 Elements of order 2:   1   2   3   4   5   6   7

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

Commutator Subloop:   0   1   5   7

Associator Subloop:   0   1   5   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 L1,8 = (2,4)(3,6) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(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