Right Bol Loop 16.3.2.11 of order 16


0123456789101112131415
1230574698111013121514
2301765411109815141312
3012647510118914151213
4576213012131415119108
5764320113121514108119
6457102314151213911810
7645031215141312810911
8101191514131223104567
9810111412151332015476
1011981315121410236745
1198101213141501327654
1214151381091176542130
1312141598111067453021
1415131210118954761203
1513121411910845670312

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

3 Elements of order 2:   2   13   14

12 Elements of order 4:   1   3   4   5   6   7   8   9   10   11   12   15

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)(12,15)(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