Right Bol Loop 16.3.2.29 of order 16


0123456789101112131415
1036725498151214111310
2341670511131289101514
3274501612141191581013
4765032115109141312118
5610347213111410815912
6507214314121315109811
7452163010158131114129
8101112151314947163520
9151214101113874056231
1081311914121510432657
1113159141081263541702
1214101513891152674013
1311981215101436210475
1412810119151325307146
1591413812111001725364

Centre:   0   4

Centrum:   0   4

Nucleus:   0   4

Left Nucleus:   0   4

Middle Nucleus:   0   4

Right Nucleus:   0   4


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:   128 (128, 1024)


/ revised October, 2001