Right Bol Loop 16.1.4.1 of order 16


0123456789101112131415
1901011121415132345867
2091110131514121438576
3111090151312144217685
4101109141213153126758
5131214159111008762134
6141512131190107583421
7151413121009116854312
8121315140101195671243
9214387650111013121514
1034216587119014151213
1143127856100915141312
1258762341131415901110
1385671432121514091011
1476853214151312111090
1567584123141213101109

Centre:   0   9

Centrum:   0   9   12   13

Nucleus:   0   9

Left Nucleus:   0   9   12   13

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.


1 Element of order 1:   0

1 Element of order 2:   9

14 Elements of order 4:   1   2   3   4   5   6   7   8   10   11   12   13   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)(4-1) neq (1*4)-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