Right Bol Loop 16.9.8.0 of order 16


0123456789101112131415
1012131191014152345687
2915141001113121437865
3101415911012134128756
4111312010915143216578
5120111315141097861432
6131101214159108754123
7159101412131105682341
8141091513120116573214
9214378560111015141312
1034128765110914151213
1143216587109013121514
1257861423151413011109
1368754132141512110910
1486573241131215109011
1575682314121314910110

Centre:   0   11

Centrum:   0   9   10   11   12   13   14   15

Nucleus:   0   11

Left Nucleus:   0   9   10   11   12   13   14   15

Middle Nucleus:   0   11

Right Nucleus:   0   11


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

9 Elements of order 2:   1   4   9   10   11   12   13   14   15

6 Elements of order 4:   2   3   5   6   7   8

Commutator Subloop:   0   11   14   15

Associator Subloop:   0   11   14   15

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,5)(3,6)(7,8)(9,12)(10,13)(14,15) is not an automorphism.   L1,1(2*2) neq L1,1(2)*L1,1(2)

Ar Property:   FAILS. The right inner mapping R1,2 = (1,7)(2,5)(3,6)(4,8) is not an automorphism.   R1,2(1*1) neq R1,2(1)*R1,2(1)

Right (Left, Full) Mult Group Orders:   64 (1024, 4096)


/ revised October, 2001