Right Bol Loop 16.3.2.33 of order 16


0123456789101112131415
1230547691181013121514
2301765411109815141312
3012674510811914151213
4576213012141315111098
5764302114151213981110
6457120313121514101189
7645031215131412891011
8101191213141521304657
9810111415121332016475
1011981312151410235746
1198101514131203127564
1213151411109875642310
1315141298111054763201
1412131510118967451023
1514121389101146570132

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

3 Elements of order 2:   2   5   6

12 Elements of order 4:   1   3   4   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,8 = (12,15)(13,14) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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