Right Bol Loop 16.5.2.16 of order 16


0123456789101112131415
1250367491381015121114
2561074313129814151011
3014725610811141391512
4307612511101415981213
5672143012151391114810
6745230115141213101198
7436501214111512810139
8101191314151205721436
9810131211141516452307
1011148915121332610745
1114151081213941503672
1213915148101154076123
1398121510111427365014
1415121110139870234561
1512131411981063147250

Centre:   0   6

Centrum:   0   6

Nucleus:   0   2   4   6

Left Nucleus:   0   1   2   3   4   5   6   7

Middle Nucleus:   0   2   4   6

Right Nucleus:   0   2   4   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   8   11   13   15

6 Elements of order 4:   2   4   9   10   12   14

4 Elements of order 8:   1   3   5   7

Commutator Subloop:   0   2   4   6

Associator Subloop:   0   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:   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:   32 (64, 256)


/ revised October, 2001