Right Bol Loop 16.3.2.20 of order 16


0123456789101112131415
1230547698111013151214
2301765411109815141312
3012674510118914121513
4675213012131415111098
5467302114151213911810
6754120313121514108119
7546031215141312891011
8101191514131223104567
9810111312151432016475
1011981415121310235746
1198101213141501327654
1214151389101175642130
1312141510118957463201
1415131298111064751023
1513121411109846570312

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   4   7

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

3 Elements of order 2:   2   5   6

12 Elements of order 4:   1   3   4   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (8,11)(9,10) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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