Right Bol Loop 16.13.2.60 of order 16


0123456789101112131415
1159101211140136854327
2140111013159127538416
3131101491210154726158
4121090151311143671285
5111314150101298217634
6915121310014111483572
7014131112915102345861
8101215914111305162743
9214837650111310121514
1034126587120149151113
1143271856139015141012
1258617342101415091311
1385762431111591401210
1467538124151210131109
1576854213141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   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:   2   3   4   5   6   8   9   10   11   12   13   14   15

2 Elements of order 4:   1   7

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)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (4,5)(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:   128 (1024, 2048)


/ revised October, 2001