Right Bol Loop 16.3.2.54 of order 16


0123456789101112131415
1230547691181013121514
2301765411109815141312
3012674510811914151213
4675031212141315810911
5467120314151213108119
6754302113121514911810
7546213015131412119108
8101191513141221307654
9810111315121432015476
1011981412151310236745
1198101214131503124567
1214151311910875642310
1312141591181054763201
1415131210811967451023
1513121481091146570132

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

3 Elements of order 2:   2   4   7

12 Elements of order 4:   1   3   5   6   8   9   10   11   12   13   14   15

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)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6) 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