Right Bol Loop 16.7.6.4 of order 16


0123456789101112131415
1230574691181013141512
2301765411109814151213
3012647510811915121314
4576231012131514111089
5764302113141215108911
6457120315121413911108
7645013214151312891110
8911101215131401327645
9111081312141512036457
1089111514121330215764
1110891413151223104576
1213141511910845670123
1314151210118957461230
1415121381091176542301
1512131498111064753012

Centre:   0   2

Centrum:   0   1   2   3   4   7

Nucleus:   0   2

Left Nucleus:   0   1   2   3   4   5   6   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.


1 Element of order 1:   0

7 Elements of order 2:   2   5   6   8   11   12   14

8 Elements of order 4:   1   3   4   7   9   10   13   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (4-1)(9-1) neq (4*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6) 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:   32 (1024, 2048)


/ revised October, 2001