Right Bol Loop 16.7.2.77 of order 16


0123456789101112131415
1230574691181014121513
2301765411109815141312
3012647510811913151214
4675213012141315810911
5467320114151213981110
6754102313121514101189
7546031215131412119108
8101191213141523104567
9810111412151330215746
1011981315121412036475
1198101514131201327654
1214151311109876540132
1312141591181057463021
1415131210811964751203
1513121489101145672310

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3

Middle Nucleus:   0   2

Right Nucleus:   0   2


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

7 Elements of order 2:   2   9   10   12   13   14   15

8 Elements of order 4:   1   3   4   5   6   7   8   11

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,8 = (8,11)(9,10) is not an automorphism.   L1,8(4*8) neq L1,8(4)*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