Right Bol Loop 16.9.2.100 of order 16


0123456789101112131415
1159101113140122584367
2141511101209131835476
3131109151210144762185
4121390141011153617258
5101215140111398126743
6901213111514107453812
7014131210915116348521
8111014159131205271634
9274381650111310121514
1034127856110914151213
1145216387109150141312
1283672541131401591011
1358761432121514901110
1461854723151210131109
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:   3   4   5   8   9   10   13   14   15

6 Elements of order 4:   1   2   6   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)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(9,14) 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