Right Bol Loop 16.9.2.126 of order 16


0123456789101112131415
1091110121514132438576
2901011131415121345867
3101190141213154126758
4111009151312143217685
5121314150101198762143
6151413121109107583412
7141512131090116854321
8131215149111005671234
9214387650111013121514
1034127586119014151213
1143216857100915141312
1258671342131514091110
1385762431121415901011
1476853214151213101190
1567584123141312111009

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9   12   13

Middle Nucleus:   0   9

Right Nucleus:   0   9


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

9 Elements of order 2:   1   2   5   6   7   8   9   12   13

6 Elements of order 4:   3   4   10   11   14   15

Commutator Subloop:   0   9

Associator Subloop:   0   9

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(7-1) neq (1*7)-1

Al Property:   FAILS. The left inner mapping L1,1 = (5,8)(12,13) is not an automorphism.   L1,1(3*5) neq L1,1(3)*L1,1(5)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001