Right Bol Loop 16.7.4.5 of order 16


0123456789101112131415
1032547698111013121514
2301765410111514981213
3210674511101415891312
4576013213128914151110
5467102312139815141011
6754320114151213101189
7645231015141312111098
8912101113141510324576
9813111012151401235467
1011148915121332670145
1110159814131223761054
1213814159101145016732
1312915148111054107623
1415101213118976453210
1514111312109867542301

Centre:   0   7

Centrum:   0   1   6   7

Nucleus:   0   7

Left Nucleus:   0   1   6   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


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

7 Elements of order 2:   1   2   3   4   5   6   7

8 Elements of order 4:   8   9   10   11   12   13   14   15

Commutator Subloop:   0   1   6   7

Associator Subloop:   0   1   6   7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

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

Al Property:   FAILS. The left inner mapping L1,8 = (2,4)(3,5) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

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

Right (Left, Full) Mult Group Orders:   64 (1024, 4096)


/ revised October, 2001