Right Bol Loop 16.11.2.43 of order 16


0123456789101112131415
1032547698111015141312
2301674510118914151213
3210765411109813121514
4567012312151314810119
5476103215121413911108
6745230114131512108911
7654321013141215119810
8911101512141301325674
9810111215131410234765
1011981314121523107456
1110891413151232016547
1215131498101145671320
1314121510119876542013
1413151211108967453102
1512141389111054760231

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