Right Bol Loop 16.5.4.5 of order 16


0123456789101112131415
1121513111014902568347
2151214101113091657438
3141301215911104216875
4131491512010113125786
5111015901214136874213
6101112091513145783124
7901014131112158342561
8091113141015127431652
9214365870111015141312
1034781256111215149013
1143872165101512130914
1287654321151413011109
1356127834149011121510
1465218743130910151211
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:   3   5   9   12   15

10 Elements of order 4:   1   2   4   6   7   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)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,1 = (3,6,5,4)(10,14,13,11) is not an automorphism.   L1,1(1*3) neq L1,1(1)*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