Right Bol Loop 16.11.2.213 of order 16


0123456789101112131415
1230574691181015121314
2301765411109814151213
3012647510811913141512
4576231012131514111089
5764302113141215911108
6457120315121413108911
7645013214151312891110
8911101415131203127645
9111081512141310235764
1089111314121532016457
1110891213151421304576
1213141589101146570123
1314151291181054763012
1415121311109875642301
1512131410811967451230

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   4   7

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   5   6   8   9   10   11   12   13   14   15

4 Elements of order 4:   1   3   4   7

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 = (8,11)(9,10) 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