Right Bol Loop 16.11.2.166 of order 16


0123456789101112131415
1032547698111015141312
2301674510118913121514
3210765411109814151213
4576012312151314910118
5467103215121413811109
6754230113141215118910
7645321014131512109811
8911101512131401324675
9810111215141310235764
1011981413121523106457
1110891314151232017546
1215131498101145761230
1314121511108967543012
1413151210119876452103
1512141389111054670321

Centre:   0   1

Centrum:   0   1

Nucleus:   0   1

Left Nucleus:   0   1   2   3

Middle Nucleus:   0   1

Right Nucleus:   0   1


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:   1   2   3   4   5   6   7   8   9   13   14

4 Elements of order 4:   10   11   12   15

Commutator Subloop:   0   1

Associator Subloop:   0   1

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-1

Al Property:   FAILS. The left inner mapping L2,8 = (12,15)(13,14) is not an automorphism.   L2,8(4*8) neq L2,8(4)*L2,8(8)

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

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001