Right Bol Loop 16.13.2.27 of order 16


0123456789101112131415
1091011121415136345827
2901113101514127483516
3101109141213154162758
4111091501312143217685
5121314015101198671234
6141512101309111538472
7151413121190102854361
8131215149111005726143
9214837650111310121514
1034126587120149151113
1143271856139015141012
1258617342101415091311
1385762431111591401210
1467538124151210131109
1576854213141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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

13 Elements of order 2:   1   2   3   6   7   8   9   10   11   12   13   14   15

2 Elements of order 4:   4   5

Commutator Subloop:   0   15

Associator Subloop:   0   15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(9,14) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

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