Right Bol Loop 16.9.2.180 of order 16


0123456789101112131415
1036274598151411121310
2457160311121481015913
3670541214131198101512
4215037612111310159814
5764302115109131411128
6301725413141215981011
7542613010158121314119
8101114121513901764235
9151413111012810542367
1081211139141575036421
1114151091381224357016
1213915814101142615703
1312891011151463401572
1411108151291336270154
1591312148111057123640

Centre:   0   5

Centrum:   0   5

Nucleus:   0   5

Left Nucleus:   0   5

Middle Nucleus:   0   5

Right Nucleus:   0   5


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

9 Elements of order 2:   1   3   4   5   7   8   9   10   15

6 Elements of order 4:   2   6   11   12   13   14

Commutator Subloop:   0   5

Associator Subloop:   0   5

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:   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:   128 (128, 1024)


/ revised October, 2001