Right Bol Loop 16.7.2.210 of order 16


0123456789101112131415
1036274591512131011814
2457160310131581491211
3670541213119148151012
4215037612101491581113
5764302115141110131298
6301725411128159141310
7542613014813121110159
8911121315101451263470
9812101114131575436201
1012891411151363501742
1113151491081224057136
1210148151391132710564
1311915812141046175023
1415131110912810342657
1514101312811907624315

Centre:   0   5

Centrum:   0   5

Nucleus:   0   5

Left Nucleus:   0   5

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. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

7 Elements of order 2:   1   3   4   5   7   12   13

8 Elements of order 4:   2   6   8   9   10   11   14   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:   128 (128, 1024)


/ revised October, 2001