Right Bol Loop 16.9.2.303 of order 16


0123456789101112131415
1014101113915126384527
2915121011014137435816
3101115901213148162745
4111090141312155217638
5131201415111094726183
6140111312159101853472
7159131210140112548361
8121314159101103671254
9218347650111310121514
1038721456110914151213
1145216387109150141312
1283672541131401591011
1354167832121514901110
1467458123151210131109
1576583214141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   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 = (4,8)(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:   128 (1024, 2048)


/ revised October, 2001