Right Bol Loop 16.5.2.2 of order 16


0123456789101112131415
1250367491411101312158
2561074313101589141112
3014725610118151491213
4307612511129141581310
5672143012131498151011
6745230114151213101189
7436501215813121110914
8913101112141527305641
9131281014151150412736
1089111513121412036574
1110815149131203147265
1214151391110874650312
1312149815111065721403
1415111213108941563027
1511101412891336274150

Centre:   0   6

Centrum:   0   6

Nucleus:   0   6

Left Nucleus:   0   6   10   12

Middle Nucleus:   0   6

Right Nucleus:   0   6


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

5 Elements of order 2:   6   9   10   12   15

2 Elements of order 4:   2   4

8 Elements of order 8:   1   3   5   7   8   11   13   14

Commutator Subloop:   0   2   4   6

Associator Subloop:   0   2   4   6

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,1 = (8,13)(9,10)(11,14)(12,15) is not an automorphism.   L1,1(1*8) neq L1,1(1)*L1,1(8)

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

Right (Left, Full) Mult Group Orders:   64 (1024, 4096)


/ revised October, 2001