Right Bol Loop 16.13.2.36 of order 16


0123456789101112131415
1014131211915106845327
2915121013014117583416
3101101491213154762158
4111090151312143617285
5121314150101198271634
6140111310159121438572
7159101112140132354861
8131215914111005126743
9214837650111310121514
1035726481120149151113
1148671352139015141012
1253217846101415091311
1384162537111591401210
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. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

13 Elements of order 2:   1   3   4   5   7   8   9   10   11   12   13   14   15

2 Elements of order 4:   2   6

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)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (4,5)(11,12) 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