Right Bol Loop 16.9.2.364 of order 16


0123456789101112131415
1015101311149122648537
2901314101112151537648
3101312915011144176285
4111090121514133285176
5131415120910116714823
6141101591213105823714
7151211101413098462351
8129141113101507351462
9285364170111015141312
1034872156111215149013
1146281735101512130914
1287654321151413011109
1353718264149011121510
1465127843130910151211
1571463582121314910110

Centre:   0   12

Centrum:   0   12

Nucleus:   0   12

Left Nucleus:   0   10   12   14

Middle Nucleus:   0   12

Right Nucleus:   0   12


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

9 Elements of order 2:   1   2   4   5   7   8   9   12   15

6 Elements of order 4:   3   6   10   11   13   14

Commutator Subloop:   0   12

Associator Subloop:   0   12

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 = (2,7)(3,6)(4,5)(9,15)(10,14)(11,13) 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