Right Bol Loop 16.11.2.8 of order 16


0123456789101112131415
1230675491181014151312
2301547611109813121514
3012764510811915141213
4657203112141513118109
5746021313151412811910
6574310214131215109811
7465132015121314910118
8121113910151403125467
9141015118121310237654
1015914811131232016745
1113812109141521304576
1211138141591047650231
1381211151410956742013
1410159131211864571302
1591410121381175463120

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3   4   5   6   7

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

11 Elements of order 2:   2   6   7   8   9   10   11   12   13   14   15

4 Elements of order 4:   1   3   4   5

Commutator Subloop:   0   2   6   7

Associator Subloop:   0   2   6   7

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 = (4,5)(6,7)(8,14)(9,13)(10,12)(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