Right Bol Loop 16.7.2.142 of order 16


0123456789101112131415
1230574691181013151214
2301765411109815141312
3012647510811914121513
4576231012141315810911
5764302113121514981110
6457120314151213101189
7645013215131412119108
8101191513141221304567
9810111415121332015746
1011981312151410236475
1198101214131503127654
1214151381091176540312
1312141598111064751023
1415131210118957463201
1513121411910845672130

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3

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   12   13   14   15

8 Elements of order 4:   1   3   4   7   8   9   10   11

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 = (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:   64 (1024, 2048)


/ revised October, 2001