Right Bol Loop 16.1.2.14 of order 16


0123456789101112131415
1901110131415122345867
2091011121514131438576
3111090141312154217658
4101109151213143126785
5131214159111008672143
6141513121190107853421
7151412131009116584312
8121315140101195761234
9214387650111013121514
1034126587119014151312
1143217856100915141213
1258671342131514901011
1385762431121415091110
1476854213151213111090
1567583124141312101109

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9

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

1 Element of order 2:   9

14 Elements of order 4:   1   2   3   4   5   6   7   8   10   11   12   13   14   15

Commutator Subloop:   0   9

Associator Subloop:   0   9

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,1 = (6,7)(14,15) is not an automorphism.   L1,1(3*5) neq L1,1(3)*L1,1(5)

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

Right (Left, Full) Mult Group Orders:   128 (1024, 2048)


/ revised October, 2001