Right Bol Loop 16.5.2.30 of order 16


0123456789101112131415
1121514111310907358462
2150111014131298467351
3141112159013105826714
4131491201510116715823
5111015012914133284176
6101309151211144173285
7912131410110151532648
8091013111415122641537
9285364170111015141312
1035172846111215149013
1143781265101512130914
1287654321151413011109
1356218734149011121510
1464827153130910151211
1571463582121314910110

Centre:   0   12

Centrum:   0   12

Nucleus:   0   12

Left Nucleus:   0   11   12   13

Middle Nucleus:   0   12

Right Nucleus:   0   12


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

5 Elements of order 2:   2   7   9   12   15

10 Elements of order 4:   1   3   4   5   6   8   10   11   13   14

Commutator Subloop:   0   12

Associator Subloop:   0   12

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,7)(9,15) 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:   64 (1024, 2048)


/ revised October, 2001