Right Bol Loop 16.13.2.31 of order 16


0123456789101112131415
1091512141011135347826
2913121001115148436517
3101201411139157125648
4111090151413126218735
5140111513121091763284
6151113912014104852371
7121514131090113581462
8131410119151202674153
9284617350111015141312
1037824156110914151213
1143586217109013121514
1276213584151413011109
1385672341141512110910
1451738462131215109011
1564157823121314910110

Centre:   0   13

Centrum:   0   13

Nucleus:   0   13

Left Nucleus:   0   13

Middle Nucleus:   0   13

Right Nucleus:   0   13


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

13 Elements of order 2:   1   3   4   6   7   8   9   10   11   12   13   14   15

2 Elements of order 4:   2   5

Commutator Subloop:   0   13

Associator Subloop:   0   13

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:   FAILS. The left inner mapping L1,1 = (2,5)(3,6)(4,7)(9,14)(10,15)(11,12) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

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