Right Bol Loop 16.9.2.29 of order 16


0123456789101112131415
1151410111390126348527
2141511131209107453816
3131101415121098126745
4121090141311155271638
5101215901113144762183
6901210111514131835472
7091312101415112584361
8111314159101203617254
9214587630111310121514
1038167452110914151213
1145216387109150141312
1283672541131401591011
1354721836121514901110
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

9 Elements of order 2:   3   4   5   8   9   10   13   14   15

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

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(3,5)(4,8)(9,14)(10,13)(11,12) 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:   128 (1024, 2048)


/ revised October, 2001