Right Bol Loop 16.13.2.88 of order 16


0123456789101112131415
1091215101113142543786
2913111215101401634875
3101109131412154721568
4111214091315103812657
5121513140910116187342
6151091314011125278431
7131410111215098365124
8140151011129137456213
9276345810111015141312
1034781256110913121514
1145278163109014151213
1256127834151314010119
1378563412141215100911
1481456327131512119010
1563812745121413911100

Centre:   0   13

Centrum:   0   13

Nucleus:   0   13

Left Nucleus:   0   13

Middle Nucleus:   0   13

Right Nucleus:   0   13


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   3   4   5   6   7   9   10   11   12   13   14   15

2 Elements of order 4:   2   8

Commutator Subloop:   0   13

Associator Subloop:   0   13

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 = (4,6)(11,15) 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:   128 (1024, 2048)


/ revised October, 2001