Right Bol Loop 16.3.8.4 of order 16


0123456789101112131415
1250367491314158111210
2561074314121191081513
3014725611158141310912
4307612513111210915814
5672143012815131491011
6745230115109121114138
7436501210141381512119
8101412131115943571602
9131215118101436024715
1014118121591350642173
1115914101312872406531
1281013914111514260357
1312891510141167153240
1411151089131201735426
1591311141281025317064

Centre:   0   2   4   6

Centrum:   0   2   4   6   9   10   11   12

Nucleus:   0   2   4   6

Left Nucleus:   0   2   4   6   9   10   11   12

Middle Nucleus:   0   2   4   6

Right Nucleus:   0   2   4   6

1 Element of order 1:   0

3 Elements of order 2:   6   11   12

4 Elements of order 4:   2   4   9   10

8 Elements of order 8:   1   3   5   7   8   13   14   15

Commutator Subloop:   0   6

Associator Subloop:   0   6

4 Conjugacy Classes of size 1:

6 Conjugacy Classes of size 2:

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, 128)


/ revised October, 2001