Right Bol Loop 16.9.2.365 of order 16


0123456789101112131415
1091011121514132438567
2901110131415121345876
3101190141213154127685
4111009151312143216758
5121315140111098672134
6141512131009117854321
7151413121190106583412
8131214159101105761243
9214387650111013121514
1034216857119014151312
1143127586100915141213
1258761342131514091011
1385672431121415901110
1467583214151213101190
1576854123141312111009

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9   10   11

Middle Nucleus:   0   9

Right Nucleus:   0   9


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   2   5   6   7   8   9   12   13

6 Elements of order 4:   3   4   10   11   14   15

Commutator Subloop:   0   9

Associator Subloop:   0   9

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(7-1) neq (1*7)-1

Al Property:   FAILS. The left inner mapping L1,1 = (3,4)(5,8)(6,7)(10,11)(12,13)(14,15) is not an automorphism.   L1,1(3*5) neq L1,1(3)*L1,1(5)

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

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001