Right Bol Loop 16.5.2.213 of order 16


0123456789101112131415
1151410121390116548327
2141511101209137853416
3131215901110148726145
4121314159101105671238
5101101415121394162783
6901213111514101435872
7091311101415122384561
8111090141312153217654
9214587630111310121514
1034761852110914151213
1143612587109150141312
1285276341131401591011
1358127436121514901110
1467834125151210131109
1576583214141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   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:   9   10   13   14   15

10 Elements of order 4:   1   2   3   4   5   6   7   8   11   12

Commutator Subloop:   0   15

Associator Subloop:   0   15

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 L1,1 = (2,6)(9,14) 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:   128 (1024, 2048)


/ revised October, 2001