Right Bol Loop 16.5.2.270 of order 16


0123456789101112131415
1901110121415132348567
2091011131514121435876
3111090141213154216758
4101109151312143127685
5131214159101108672134
6141513121090117853412
7151412131109106584321
8121315140111095761243
9214387650111013121514
1034127856119014151312
1143216587100915141213
1258672431131514091110
1385761342121415901011
1476854213151213101109
1567583124141312111090

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9

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:   9   12   13   14   15

10 Elements of order 4:   1   2   3   4   5   6   7   8   10   11

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 = (6,7)(14,15) 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:   128 (1024, 2048)


/ revised October, 2001