Right Bol Loop 16.13.2.7 of order 16


0123456789101112131415
1091012131415112584367
2901213111514101835476
3101209151113144762185
4111314091012153617258
5131115140121098126743
6141511101209137453812
7151413111090126348521
8121091514131105271634
9218347650111310121514
1038167452110914151213
1145672381109150141312
1283216547131401591011
1354721836121514901110
1467458123151210131109
1576583214141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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

13 Elements of order 2:   1   2   3   4   5   6   7   8   9   10   13   14   15

2 Elements of order 4:   11   12

Commutator Subloop:   0   15

Associator Subloop:   0   15

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 = (3,5)(10,13) 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:   128 (1024, 2048)


/ revised October, 2001