Right Bol Loop 16.11.2.9 of order 16


0123456789101112131415
1032547698111015141312
2301674510118913121514
3210765411109814151213
4567012312151314108911
5476103215121413119810
6745230113141215810119
7654321014131512911108
8911101512141301237546
9810111215131410326457
1011981413151223015764
1110891314121532104675
1215141398111045671320
1314151211109867453102
1413121510118976542013
1512131489101154760231

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   10   11

4 Elements of order 4:   12   13   14   15

Commutator Subloop:   0   1   2   3

Associator Subloop:   0   1   2   3

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (4-1)(9-1) neq (4*9)-1

Al Property:   FAILS. The left inner mapping L2,8 = (4,5)(6,7)(8,9)(10,11)(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 (4096, 16384)


/ revised October, 2001