Right Bol Loop 16.5.4.9 of order 16


0123456789101112131415
1250367498111213101514
2561074313101489151211
3014725610138915141112
4307612511129151481013
5672143012111514891310
6745230115141213101198
7436501214151310111289
8101191314151261523470
9810131211141570234561
1011148915121352670143
1114151081213925701634
1213915148101134016725
1398121510111443167052
1415121110139816452307
1512131411981007345216

Centre:   0   6

Centrum:   0   6   10   12

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.


1 Element of order 1:   0

5 Elements of order 2:   6   9   11   13   14

6 Elements of order 4:   2   4   8   10   12   15

4 Elements of order 8:   1   3   5   7

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 = (8,11)(9,12)(10,14)(13,15) is not an automorphism.   L1,1(1*9) neq L1,1(1)*L1,1(9)

Ar Property:   FAILS. The right inner mapping R1,8 = (1,3)(2,4)(5,7)(8,11)(9,14)(13,15) is not an automorphism.   R1,8(1*8) neq R1,8(1)*R1,8(8)

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


/ revised October, 2001