Right Bol Loop 16.3.4.9 of order 16


0123456789101112131415
1230745698111014151213
2301674511109813121514
3012567410118915141312
4765032115131214109118
5476321012141513811910
6547210314121315910811
7654103213151412118109
8121113151014947563120
9151014138121174652031
1014915121113856470213
1113812149151065741302
1211138101491532014675
1381211915101410236457
1491510111381223107546
1510149812111301325764

Centre:   0   2

Centrum:   0   2   4   6

Nucleus:   0   2

Left Nucleus:   0   2   4   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   4   6

12 Elements of order 4:   1   3   5   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   2   4   6

Associator Subloop:   0   2   4   6

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,6)(5,7)(8,14)(9,12)(10,13)(11,15) 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, 4096)


/ revised October, 2001