Right Bol Loop 16.13.2.55 of order 16


0123456789101112131415
1091311121415106354827
2901213101514117438516
3101215149111304126758
4111314015101293271685
5121091501311148617234
6141511101309121583472
7151410121190132845361
8131109141210155762143
9214837650111310121514
1035162487120149151113
1148217356139015141012
1253671842101415091311
1384726531111591401210
1467538124151210131109
1576854213141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   10   13   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   4   5   6   7   9   10   11   12   13   14   15

2 Elements of order 4:   3   8

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)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(3,8)(4,5)(9,14)(10,13)(11,12) 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:   64 (1024, 2048)


/ revised October, 2001