Right Bol Loop 16.11.2.238 of order 16


0123456789101112131415
1230574691181013151214
2301765411109815141312
3012647510811914121513
4675031212141315119108
5467102313121514101189
6754320114151213981110
7546213015131412810911
8101191213141523107654
9810111315121430216475
1011981412151312035746
1198101514131201324567
1213151481091175640312
1315141298111067451023
1412131510118954763201
1514121311910846572130

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

11 Elements of order 2:   2   4   5   6   7   9   10   12   13   14   15

4 Elements of order 4:   1   3   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 = (4,7)(5,6)(8,11)(9,10)(12,15)(13,14) 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