Right Bol Loop 16.5.2.9 of order 16


0123456789101112131415
1091110121514132436758
2901011131415121347685
3101109151312144128567
4111090141213153215876
5121314159111008673421
6141513121090117852143
7151412131109106581234
8131215140101195764312
9214387650111013121514
1034217586119014151312
1143126857100915141213
1258762341131514901011
1385671432121415091110
1467583124151213111090
1576854213141312101109

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9   12   13

Middle Nucleus:   0   9   10   11

Right Nucleus:   0   9   10   11


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   3   4   9

10 Elements of order 4:   5   6   7   8   10   11   12   13   14   15

Commutator Subloop:   0   9   10   11

Associator Subloop:   0   9   10   11

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (5,6,8,7)(12,15,13,14) is not an automorphism.   L1,1(5*1) neq L1,1(5)*L1,1(1)

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

Right (Left, Full) Mult Group Orders:   32 (512, 2048)


/ revised October, 2001