Right Bol Loop 16.7.2.433 of order 16


0123456789101112131415
1230574691181014121513
2301765411109815141312
3012647510811913151214
4576231012141315119108
5764302114151213101189
6457120313121514981110
7645013215131412810911
8101191513141223107564
9810111312151430216745
1011981415121312035476
1198101214131501324657
1213151489101176540312
1315141210811957463201
1412131591181064751023
1514121311109845672130

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3   4   5   6   7

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

7 Elements of order 2:   2   5   6   9   10   12   15

8 Elements of order 4:   1   3   4   7   8   11   13   14

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6)(8,11)(9,10)(12,15)(13,14) 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:   32 (1024, 2048)


/ revised October, 2001