Right Bol Loop 16.5.4.2 of order 16


0123456789101112131415
1012111014131592438657
2915101113141201347568
3101490121513114786125
4111309151214103875216
5131112159010146124783
6141015120911135213874
7159141311100128652431
8120131410119157561342
9214365870111015141312
1034127856111215149013
1143218765101512130914
1287654321151413011109
1356781234149011121510
1465872143130910151211
1578563412121314910110

Centre:   0   15

Centrum:   0   9   12   15

Nucleus:   0   15

Left Nucleus:   0   9   12   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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

5 Elements of order 2:   1   7   9   12   15

10 Elements of order 4:   2   3   4   5   6   8   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)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,8)(9,12) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

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

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


/ revised October, 2001