Right Bol Loop 16.7.2.209 of order 16


0123456789101112131415
1230547691181013121514
2301765411109815141312
3012674510811914151213
4675031212141315810911
5467120313121514911810
6754302114151213108119
7546213015131412119108
8101191213141521304657
9810111312151432015746
1011981415121310236475
1198101514131203127564
1213151481091176540132
1315141291181064751023
1412131510811957463201
1514121311910845672310

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   4   7

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

7 Elements of order 2:   2   4   7   12   13   14   15

8 Elements of order 4:   1   3   5   6   8   9   10   11

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6) is not an automorphism.   L1,8(4*8) neq L1,8(4)*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, 2048)


/ revised October, 2001