Right Bol Loop 16.7.2.3 of order 16


0123456789101112131415
1230764598111015141312
2301547611109813121514
3012675410118914151213
4756201312151413811109
5647023113141512118910
6475130215121314910118
7564312014131215109811
8121113910141521304567
9141015118131230216745
1015914811121312037654
1113812109151403125476
1211138141510956740213
1381211151491047652031
1410159131281165473120
1591410121311874561302

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)(8,14)(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