Right Bol Loop 16.9.8.1 of order 16


0123456789101112131415
1101109141315122345687
2111090151214131436578
3091011121513144128756
4901110131412153217865
5141512131091106871234
6151413121101095782143
7131215149100118654321
8121314150119107563412
9214365870111013121514
1034128765110914151213
1143217856109015141312
1256871243131415091011
1365782134121514901110
1487563421151213101109
1578654312141312111090

Centre:   0   10

Centrum:   0   9   10   11   12   13   14   15

Nucleus:   0   10

Left Nucleus:   0   9   10   11   12   13   14   15

Middle Nucleus:   0   10

Right Nucleus:   0   10


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

9 Elements of order 2:   6   7   9   10   11   12   13   14   15

6 Elements of order 4:   1   2   3   4   5   8

Commutator Subloop:   0   10

Associator Subloop:   0   10

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(7-1) neq (1*7)-1

Al Property:   FAILS. The left inner mapping L1,1 = (6,7)(13,15) is not an automorphism.   L1,1(2*5) neq L1,1(2)*L1,1(5)

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

Right (Left, Full) Mult Group Orders:   32 (1024, 2048)


/ revised October, 2001