Right Bol Loop 16.3.8.1 of order 16


0123456789101112131415
1032548967131211101514
2310681151241497151310
3201861241151579141013
4579101314215312101168
5497131015314211011286
6811121415113010732954
7954231311006151481112
8612111514010113923745
9745321001318141561211
1013141512117698054123
1112861031521451013497
1211680121431541310579
1310151411129876145032
1415131079511412286310
1514101397412511368201

Centre:   0   1   10   13

Centrum:   0   1   6   7   8   9   10   13

Nucleus:   0   1   10   13

Left Nucleus:   0   1   6   7   8   9   10   13

Middle Nucleus:   0   1   10   13

Right Nucleus:   0   1   10   13

1 Element of order 1:   0

3 Elements of order 2:   1   10   13

12 Elements of order 4:   2   3   4   5   6   7   8   9   11   12   14   15

Commutator Subloop:   0   10

Associator Subloop:   0   10

4 Conjugacy Classes of size 1:

6 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(5-1) neq (2*5)-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