Right Bol Loop 16.7.2.5 of order 16


0123456789101112131415
1230675491514108111312
2301547611109813121514
3012764510141591181213
4657203112811131514109
5746021313118121415910
6574310214131215109811
7465132015121314910118
8121113910151424501376
9141015118121330217645
1015914811131212036754
1113812109141505423167
1211138141591057640213
1381211151410946752031
1410159131211873165420
1591410121381161374502

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   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

7 Elements of order 2:   2   6   7   9   10   12   13

8 Elements of order 4:   1   3   4   5   8   11   14   15

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:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (4,5)(6,7)(8,11)(9,10)(12,13)(14,15) 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 (4096, 16384)


/ revised October, 2001