Right Bol Loop 16.13.2.28 of order 16


0123456789101112131415
1091211131015145643287
2901112141510138734156
3101509111413127821465
4111213141090156512378
5131415100111291467823
6121114131509104158732
7151090121314113285641
8141310159121102376514
9217684350111015141312
1037824156110914151213
1146283517109013121514
1264157823151413011109
1358431762141512110910
1485672341131215109011
1573516284121314910110

Centre:   0   14

Centrum:   0   14

Nucleus:   0   14

Left Nucleus:   0   14

Middle Nucleus:   0   14

Right Nucleus:   0   14


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   2   3   5   6   8   9   10   11   12   13   14   15

2 Elements of order 4:   4   7

Commutator Subloop:   0   14

Associator Subloop:   0   14

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 L1,1 = (2,5)(9,13) 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