Right Bol Loop 16.9.4.53 of order 16


0123456789101112131415
1091110131415122438657
2901011141312151347568
3101109121513144786125
4111090151214133875216
5131415129010116124783
6141312150911105213874
7151214131011098652431
8121513141110907561342
9214365870111015141312
1034218756111215149013
1143127865101512130914
1287654321151413011109
1356872134149011121510
1465781243130910151211
1578563412121314910110

Centre:   0   9

Centrum:   0   9   12   15

Nucleus:   0   9

Left Nucleus:   0   9   12   15

Middle Nucleus:   0   9

Right Nucleus:   0   9


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

9 Elements of order 2:   1   2   3   4   7   8   9   12   15

6 Elements of order 4:   5   6   10   11   13   14

Commutator Subloop:   0   9   12   15

Associator Subloop:   0   9   12   15

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (5,6)(13,14) is not an automorphism.   L1,1(3*5) neq L1,1(3)*L1,1(5)

Ar Property:   FAILS. The right inner mapping R1,3 = (3,5)(4,6)(10,13)(11,14) is not an automorphism.   R1,3(1*3) neq R1,3(1)*R1,3(3)

Right (Left, Full) Mult Group Orders:   64 (4096, 16384)


/ revised October, 2001