Right Bol Loop 16.7.2.363 of order 16


0123456789101112131415
1230547691181015141312
2301765411109814151213
3012674510811913121514
4675231012131514810119
5467320113141215108911
6754102315121413911108
7546013214151312119810
8911101413151203127546
9111081512141310235764
1089111314121532016457
1110891215131421304675
1215141381091146572301
1312151491181054761032
1413121511910875640123
1514131210811967453210

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

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   8   9   10   11   13   15

8 Elements of order 4:   1   3   4   5   6   7   12   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.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6)(8,11)(9,10)(12,14)(13,15) 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:   128 (1024, 2048)


/ revised October, 2001