Right Bol Loop 16.15.2.8 of order 16


0123456789101112131415
1032547698111015141312
2301674510118914151213
3210765411109813121514
4567012312151314810119
5476103215121413911108
6745230113141215119810
7654321014131512108911
8911101512131401234765
9810111215141310325674
1011981413121523017456
1110891314151232106547
1215141398101145670321
1314151211108967453012
1413121510119876542103
1512131489111054761230

Centre:   0   1

Centrum:   0   1

Nucleus:   0   1

Left Nucleus:   0   1   4   5

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.


1 Element of order 1:   0

15 Elements of order 2:   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   1

Associator Subloop:   0   1

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L2,8 = (8,9)(10,11) 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