Right Bol Loop 16.1.2.4 of order 16


0123456789101112131415
1101190151413122347856
2111009141512131438765
3901110131214154215687
4091011121315143126578
5151413121110096784321
6141512131011905873412
7131214150910118652134
8121315149011107561243
9214365870111013121514
1034217865119014151312
1143128756100915141213
1256782143131514901011
1365871234121415091110
1487563421151213111090
1578654312141312101109

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9   12   13

Middle Nucleus:   0   9   10   11

Right Nucleus:   0   9   10   11


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

1 Element of order 2:   9

6 Elements of order 4:   10   11   12   13   14   15

8 Elements of order 8:   1   2   3   4   5   6   7   8

Commutator Subloop:   0   9   10   11

Associator Subloop:   0   9   10   11

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(6-1) neq (1*6)-1

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

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

Right (Left, Full) Mult Group Orders:   32 (512, 2048)


/ revised October, 2001