Right Bol Loop 16.9.2.176 of order 16


0123456789101112131415
1159131210140112584367
2140121011159131835476
3131115140121094762185
4121014091311153617258
5101209151113148126743
6915111312014107453812
7014101113915126348521
8111391514101205271634
9214587630111310121514
1034127856110914151213
1143276581109150141312
1285612347131401591011
1358761432121514901110
1467834125151210131109
1576583214141312111090

Centre:   0   15

Centrum:   0   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:   2   4   6   8   9   10   13   14   15

6 Elements of order 4:   1   3   5   7   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 = (2,6)(3,5)(4,8)(9,14)(10,13)(11,12) 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