Right Bol Loop 16.7.2.114 of order 16


0123456789101112131415
1230574691181013151214
2301765411109815141312
3012647510811914121513
4675013212141315111098
5467120313121514108119
6754302114151213911810
7546231015131412891011
8101191213141523107654
9810111315121430216475
1011981412151312035746
1198101514131201324567
1213151489101175640132
1315141291181067451203
1412131510811954763021
1514121311109846572310

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3

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   9   10   12   15

8 Elements of order 4:   1   3   5   6   8   11   13   14

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6)(8,11)(9,10)(12,15)(13,14) 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