Right Bol Loop 16.9.2.205 of order 16


0123456789101112131415
1151410111390126584327
2140121311159107835416
3131215140111098762145
4121090141311155617238
5101109151213144126783
6915111012014131453872
7091312101415112348561
8111314159101203271654
9278541630111310121514
1034761852110914151213
1145216387109150141312
1283672541131401591011
1358127436121514901110
1461438725151210131109
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

9 Elements of order 2:   2   4   6   8   9   10   13   14   15

6 Elements of order 4:   1   3   5   7   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)(3-1) neq (1*3)-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