Right Bol Loop 16.5.2.49 of order 16


0123456789101112131415
1091110121514132438576
2901011131415121345867
3101190141312154127658
4111009151213143216785
5121315149101108671243
6141513121109107853412
7151412131090116584321
8131214150111095762134
9214387650111013121514
1034126587119014151312
1143217856100915141213
1258672431131514901011
1385761342121415091110
1467584213151213111090
1576853124141312101109

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9   14   15

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

5 Elements of order 2:   1   2   6   7   9

10 Elements of order 4:   3   4   5   8   10   11   12   13   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