Right Bol Loop 16.9.2.36 of order 16


0123456789101112131415
1032547698121510141311
2406173510128139111514
3517062411151381410129
4260715312109148151113
5371604215111491312108
6745230113141110158912
7654321014131512119810
8910111215131406243175
9811101512141317425063
1012813914111523016457
1115914813101232670541
1210138149151145107236
1314121510118960352714
1413151211109871534602
1511149138121054761320

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   2   5   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


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   5   6   7   8   10   14   15

6 Elements of order 4:   3   4   9   11   12   13

Commutator Subloop:   0   7

Associator Subloop:   0   7

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:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (128, 512)


/ revised October, 2001