Right Bol Loop 16.3.2.98 of order 16


0123456789101112131415
1036725498121311101514
2341670510121589141311
3274501612101491581113
4765032115141110131298
5610347213119148151012
6507214311138151491210
7452163014151312101189
8911131512101447263510
9813101411121574356201
1012814119151365401732
1113159101481223047156
1210981315141156714023
1311141512891032170465
1415121191013810532647
1514101281311901625374

Centre:   0   4

Centrum:   0   4

Nucleus:   0   4   8   15

Left Nucleus:   0   3   4   5   8   12   13   15

Middle Nucleus:   0   4   8   15

Right Nucleus:   0   4   8   15


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

3 Elements of order 2:   1   4   7

12 Elements of order 4:   2   3   5   6   8   9   10   11   12   13   14   15

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-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:   32 (64, 256)


/ revised October, 2001