Right Bol Loop 16.11.2.255 of order 16


0123456789101112131415
1230574698111015141312
2301765411109814151213
3012647510118913121514
4576231012151314119810
5764302115121413108911
6457120313141215911108
7645013214131512810119
8911101415131201327546
9111081314121510236457
1089111512141332015764
1110891213151423104675
1215141381091145670321
1312151410118967453012
1413121511910876542103
1514131298111054761230

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 = (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:   64 (1024, 2048)


/ revised October, 2001