Right Bol Loop 16.13.2.103 of order 16


0123456789101112131415
1032547691512131110814
2406173510131589141211
3517062412101491581113
4260715313119148151012
5371604211128151491310
6745230114813121011159
7654321015141110131298
8911121310141506524317
9813101112151410432576
1013151498121123076145
1112891415131054701632
1211141589101335160724
1310981514111242617053
1415121110138967345201
1514101312119871253460

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


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

13 Elements of order 2:   1   2   5   6   7   8   9   10   11   12   13   14   15

2 Elements of order 4:   3   4

Commutator Subloop:   0   7

Associator Subloop:   0   7

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (128, 1024)


/ revised October, 2001