Right Bol Loop 16.3.8.2 of order 16


0123456789101112131415
1032548967111013121514
2310681051149715141213
3201861141057914151312
4579103122131514861011
5497012133121415681110
6810113215014113124597
7954121301511423111086
8611102314115012135479
9745131211401532101168
1011861514132123107945
1110681415123132019754
1213151497411510681023
1312141579510411860132
1415121310119876452301
1514131211107698543210

Centre:   0   1   14   15

Centrum:   0   1   6   7   8   9   14   15

Nucleus:   0   1   14   15

Left Nucleus:   0   1   6   7   8   9   14   15

Middle Nucleus:   0   1   14   15

Right Nucleus:   0   1   14   15

1 Element of order 1:   0

3 Elements of order 2:   1   14   15

12 Elements of order 4:   2   3   4   5   6   7   8   9   10   11   12   13

Commutator Subloop:   0   15

Associator Subloop:   0   15

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