Right Bol Loop 16.11.6.3 of order 16


0123456789101112131415
1230574691181013141512
2301765411109814151213
3012647510811915121314
4576231012131514111089
5764302113141215108911
6457120315121413911108
7645013214151312891110
8911101215131403127546
9111081312141510236754
1089111514121332015467
1110891413151221304675
1213141511910846570321
1314151210118954761032
1415121381091175642103
1512131498111067453210

Centre:   0   2

Centrum:   0   1   2   3   4   7

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.


1 Element of order 1:   0

11 Elements of order 2:   2   5   6   8   9   10   11   12   13   14   15

4 Elements of order 4:   1   3   4   7

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 = (4,7)(5,6)(8,11)(9,10)(12,14)(13,15) 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:   32 (1024, 2048)


/ revised October, 2001