Right Bol Loop 16.7.2.369 of order 16


0123456789101112131415
1230547691181013121514
2301765411109815141312
3012674510811914151213
4576031212141315891011
5764120313121514981110
6457302114151213101189
7645213015131412111098
8101191513141221304567
9810111412151332015476
1011981315121410236745
1198101214131503127654
1214151311109876540132
1312141510118964751023
1415131298111057463201
1513121489101145672310

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   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 = (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:   128 (1024, 2048)


/ revised October, 2001