Right Bol Loop 16.9.2.79 of order 16


0123456789101112131415
1032547698131211101514
2406173510121581491311
3517062412109148151113
4260715313111491581012
5371604211138159141210
6745230114151213101189
7654321015141110131298
8911121310141506524317
9813101112151417342506
1013151498121124071635
1112891415131053706142
1211141589101335617024
1310981514111242160753
1415121110138960435271
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

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

6 Elements of order 4:   3   4   9   12   13   14

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