Right Bol Loop 16.5.4.37 of order 16


0123456789101112131415
1121514111310907358462
2151213101411098467351
3141301591211105826714
4131491201510116715823
5111015012914133284176
6101112915013144173285
7901114101312151532648
8091013111415122641537
9214365870111015141312
1034872156111215149013
1143781265101512130914
1287654321151413011109
1356218734149011121510
1465127843130910151211
1578563412121314910110

Centre:   0   12

Centrum:   0   10   12   14

Nucleus:   0   12

Left Nucleus:   0   9   10   11   12   13   14   15

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:   3   6   9   12   15

10 Elements of order 4:   1   2   4   5   7   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)(5-1) neq (1*5)-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:   32 (1024, 2048)


/ revised October, 2001