Right Bol Loop 16.11.2.23 of order 16


0123456789101112131415
1230547691181015141312
2301765411109814151213
3012674510811913121514
4576013212131514891110
5764102315121413981011
6457320113141215101198
7645231014151312111089
8911101413151203127546
9111081314121510236457
1089111512141332015764
1110891215131421304675
1215141311109845672301
1312151498111064751032
1413121589101176540123
1514131210118957463210

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

11 Elements of order 2:   2   4   5   6   7   8   9   10   11   13   15

4 Elements of order 4:   1   3   12   14

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,8 = (8,11)(9,10) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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