Right Bol Loop 16.9.2.434 of order 16


0123456789101112131415
1091110131514122435876
2901011121415131348567
3101109151213144126758
4111090141312153217685
5121314150111098672143
6141513121009117854312
7151412131190106583421
8131215149101105761234
9214387650111013121514
1034216857119014151312
1143127586100915141213
1258762341131514901011
1385671432121415091110
1467584213151213111090
1576853124141312101109

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9   10   11   12   13   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

9 Elements of order 2:   1   2   3   4   5   6   7   8   9

6 Elements of order 4:   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)(4-1) neq (1*4)-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:   32 (1024, 2048)


/ revised October, 2001