Right Bol Loop 16.1.2.7 of order 16


0123456789101112131415
1250367491415813111012
2561074314101291181513
3014725611814131512910
4307612513119121015814
5672143010151314891211
6745230115121110914138
7436501212138151410119
8101312149151165173420
9151113101412876240351
1013981215111434602175
1114121598101352064713
1281014111391510426537
1391510811141221357604
1412811151013947531062
1511149131281003715246

Centre:   0   6

Centrum:   0   6

Nucleus:   0   2   4   6

Left Nucleus:   0   1   2   3   4   5   6   7

Middle Nucleus:   0   2   4   6

Right Nucleus:   0   2   4   6


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

1 Element of order 2:   6

10 Elements of order 4:   2   4   8   9   10   11   12   13   14   15

4 Elements of order 8:   1   3   5   7

Commutator Subloop:   0   2   4   6

Associator Subloop:   0   6

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-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:   32 (64, 256)


/ revised October, 2001