Right Bol Loop 16.13.2.5 of order 16


0123456789101112131415
1129101115131402348675
2150141312111091435768
3131401511129104126857
4141315010912113217586
5912111001413158762431
6101112914015137853124
7111091213150146584213
8015131491011125671342
9217684350111015141312
1037154826110913121514
1146513287109014151213
1285672341151314010119
1364827153141215100911
1473286514131512119010
1558431762121413911100

Centre:   0   12

Centrum:   0   12

Nucleus:   0   12

Left Nucleus:   0   12

Middle Nucleus:   0   12

Right Nucleus:   0   12


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:   2   3   4   5   6   7   9   10   11   12   13   14   15

2 Elements of order 4:   1   8

Commutator Subloop:   0   12

Associator Subloop:   0   12

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)(9,15)(10,13)(11,14) 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