Right Bol Loop 16.7.2.7 of order 16


0123456789101112131415
1230574691181013141512
2301765411109814151213
3012647510811915121314
4576013212151314119810
5764120315141213981011
6457302113121415101198
7645231014131512810119
8911101413151230217546
9111081312141501325467
1089111514121323106754
1110891215131412034675
1215141311109864750321
1312151491181076541032
1413121589101157462103
1514131210811945673210

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   5   6

Middle Nucleus:   0   1   2   3

Right Nucleus:   0   1   2   3


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   4   7   12   13   14   15

4 Elements of order 4:   1   3   5   6

4 Elements of order 8:   8   9   10   11

Commutator Subloop:   0   1   2   3

Associator Subloop:   0   1   2   3

2 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 2:

2 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(13-1) neq (1*13)-1

Al Property:   FAILS. The left inner mapping L4,8 = (8,9,11,10)(12,13,14,15) is not an automorphism.   L4,8(4*8) neq L4,8(4)*L4,8(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   32 (512, 2048)


/ revised October, 2001