Right Bol Loop 16.5.4.20 of order 16


0123456789101112131415
1015101311149122648537
2912111410130151537648
3101112159013144176285
4111015120914133285176
5131490121510116714823
6141309151211105823714
7150131014111298462351
8129141113101507351462
9214365870111015141312
1035827146111215149013
1146718235101512130914
1287654321151413011109
1353281764149011121510
1464172853130910151211
1578563412121314910110

Centre:   0   12

Centrum:   0   9   12   15

Nucleus:   0   12

Left Nucleus:   0   9   12   15

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.


1 Element of order 1:   0

5 Elements of order 2:   1   8   9   12   15

10 Elements of order 4:   2   3   4   5   6   7   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)(3-1) neq (1*3)-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