Right Bol Loop 16.3.2.43 of order 16


0123456789101112131415
1230574698111014151213
2301765411109815141312
3012647510118913121514
4576231012131415111098
5764302114151213101189
6457120313121514981110
7645013215141312891011
8101191213141523104567
9810111412151332015476
1011981315121410236745
1198101514131201327654
1213151411910875642130
1315141298111057461203
1412131510118964753021
1514121381091146570312

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.


1 Element of order 1:   0

3 Elements of order 2:   2   5   6

12 Elements of order 4:   1   3   4   7   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 = (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:   64 (1024, 2048)


/ revised October, 2001