Right Bol Loop 16.3.4.6 of order 16


0123456789101112131415
1032547698121310111514
2310675410128159141311
3201764512109148151113
4567012314151312111089
5476103215141110131298
6754231013111491581012
7645320111131581491210
8911131415121010362754
9813111514101201273645
1012141513118932140576
1113981210151467415023
1210151411139823051467
1311891012141576504132
1415121089111354726310
1514101298131145637201

Centre:   0   1   4   5

Centrum:   0   1   4   5

Nucleus:   0   1   4   5

Left Nucleus:   0   1   4   5

Middle Nucleus:   0   1   4   5

Right Nucleus:   0   1   4   5

1 Element of order 1:   0

3 Elements of order 2:   1   4   5

12 Elements of order 4:   2   3   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   1   4   5

Associator Subloop:   0   1   4   5

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*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 (256, 1024)


/ revised October, 2001