Right Bol Loop 16.9.4.21 of order 16


0123456789101112131415
1036274598131210111514
2457160310131581491211
3670541213101498151112
4215037612119141581013
5764302115141110131298
6301725411128159141310
7542613014151213111089
8911121315101451263470
9812101114131570346251
1012891411151363501742
1113151491081224057136
1210148151391136170524
1311915812141042715063
1415131110912815432607
1514101312811907624315

Centre:   0   5

Centrum:   0   5   12   13

Nucleus:   0   5

Left Nucleus:   0   5   12   13

Middle Nucleus:   0   5

Right Nucleus:   0   5


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:   1   3   4   5   7   9   12   13   14

6 Elements of order 4:   2   6   8   10   11   15

Commutator Subloop:   0   5

Associator Subloop:   0   5

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

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

Right (Left, Full) Mult Group Orders:   64 (128, 512)


/ revised October, 2001