Right Bol Loop 16.5.4.6 of order 16


0123456789101112131415
1121510111413902348567
2151211101314091437658
3141390151211104876215
4131409121510113785126
5111012150914136214873
6101115129013145123784
7901314111012158562341
8091413101115127651432
9214365870111015141312
1034218756111215149013
1143127865101512130914
1287654321151413011109
1356872134149011121510
1465781243130910151211
1578563412121314910110

Centre:   0   9

Centrum:   0   9   12   15

Nucleus:   0   9

Left Nucleus:   0   9   12   15

Middle Nucleus:   0   9

Right Nucleus:   0   9


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

5 Elements of order 2:   5   6   9   12   15

10 Elements of order 4:   1   2   3   4   7   8   10   11   13   14

Commutator Subloop:   0   9   12   15

Associator Subloop:   0   9   12   15

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (3,6,4,5)(10,14,11,13) is not an automorphism.   L1,1(1*3) neq L1,1(1)*L1,1(3)

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