Right Bol Loop 16.11.2.219 of order 16


0123456789101112131415
1230574691181015121314
2301765411109814151213
3012647510811913141512
4675013212131514810119
5467120315121413981011
6754302113141215101198
7546231014151312119810
8911101415131203124576
9111081314121510235764
1089111512141332016457
1110891213151421307645
1213141511910845670123
1314151298111064753012
1415121381091176542301
1512131410118957461230

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

11 Elements of order 2:   2   4   7   8   9   10   11   12   13   14   15

4 Elements of order 4:   1   3   5   6

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6)(8,11)(9,10)(12,14)(13,15) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001