Right Bol Loop 16.11.4.20 of order 16


0123456789101112131415
1032547698111013121514
2301765410138141591112
3210674511129151481013
4576013215141213101198
5467102314151312111089
6754320113101489151211
7645231012111598141310
8912131514111041762350
9813121415101150673241
1011151412139876410532
1110141513128967501423
1213891011141523054167
1312981110151432145076
1415111098121314326705
1514101189131205237614

Centre:   0   4

Centrum:   0   1   4   5

Nucleus:   0   4

Left Nucleus:   0   1   4   5

Middle Nucleus:   0   4

Right Nucleus:   0   4


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

11 Elements of order 2:   1   2   3   4   5   6   7   9   11   13   14

4 Elements of order 4:   8   10   12   15

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (8,15)(9,14) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001