Right Bol Loop 16.9.4.2 of order 16


0123456789101112131415
1014151211910135362847
2915141310011128471536
3101213149110156154728
4111312150109147283615
5121011015131491638274
6140910131512113517482
7159011121413104826351
8131110914121502745163
9214387650111013121514
1034126587110914151213
1143217856109015141312
1258671342131415091011
1385762431121514901110
1467583124151213101109
1576854213141312111090

Centre:   0   13

Centrum:   0   10   13   15

Nucleus:   0   13

Left Nucleus:   0   9   10   11   12   13   14   15

Middle Nucleus:   0   13

Right Nucleus:   0   13


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   8   9   10   11   12   13   14   15

6 Elements of order 4:   2   3   4   5   6   7

Commutator Subloop:   0   10   13   15

Associator Subloop:   0   10   13   15

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,4)(3,7)(5,6)(9,11)(10,15)(12,14) is not an automorphism.   L1,1(2*2) neq L1,1(2)*L1,1(2)

Ar Property:   FAILS. The right inner mapping R1,2 = (1,3)(2,4)(5,6)(7,8) is not an automorphism.   R1,2(1*1) neq R1,2(1)*R1,2(1)

Right (Left, Full) Mult Group Orders:   64 (1024, 4096)


/ revised October, 2001