Right Bol Loop 16.13.2.86 of order 16


0123456789101112131415
1091311121415106845327
2901110131514127583416
3101101491213154762158
4111014150131293617285
5121390151011148271634
6141512131009111438572
7151410121190132354861
8131215914111005126743
9215387640111310121514
1034762581120149151113
1143271856139015141012
1258617342101415091311
1385126437111591401210
1467483125151210131109
1576854213141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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

13 Elements of order 2:   1   2   3   6   7   8   9   10   11   12   13   14   15

2 Elements of order 4:   4   5

Commutator Subloop:   0   15

Associator Subloop:   0   15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(9,14) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

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