Right Bol Loop 16.9.4.19 of order 16


0123456789101112131415
1014131210915116384527
2915121011014137435816
3101215140111398162745
4111314091012155217638
5131109151210144726183
6140111312159101853472
7159101113140122548361
8121091514131103671254
9214587630111310121514
1034127856110914151213
1143276581109150141312
1285612347131401591011
1358761432121514901110
1467834125151210131109
1576583214141312111090

Centre:   0   15

Centrum:   0   10   13   15

Nucleus:   0   15

Left Nucleus:   0   10   13   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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   4   7   8   9   10   13   14   15

6 Elements of order 4:   2   3   5   6   11   12

Commutator Subloop:   0   15

Associator Subloop:   0   15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,1 = (3,5)(10,13) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

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