Right Bol Loop 16.13.2.46 of order 16


0123456789101112131415
1151410121190132854367
2140121013159111538476
3131201491110155726148
4121014015131198671235
5111391501012143217684
6915111310014127483512
7091311121415106345821
8101115914121304162753
9275831640111310121514
1034126587120149151113
1148671352139015141012
1253217846101415091311
1385762431111591401210
1461438725151210131109
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:   2   3   4   5   6   8   9   10   11   12   13   14   15

2 Elements of order 4:   1   7

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