Right Bol Loop 16.3.2.75 of order 16


0123456789101112131415
1230574698111013121514
2301765411109815141312
3012647510118914151213
4675213012131415111098
5467320113121514101189
6754102314151213981110
7546031215141312891011
8101191513141221304567
9810111415121330215476
1011981312151412036745
1198101214131503127654
1213151489101175642310
1315141291181064753201
1412131510811957461023
1514121311109846570132

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   5   6

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   9   10

12 Elements of order 4:   1   3   4   5   6   7   8   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)(5-1) neq (1*5)-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