Right Bol Loop 16.13.2.23 of order 16


0123456789101112131415
1012101113914152346578
2901113151412101437865
3101514120111394128756
4111012091315143215687
5131109141510128764132
6121415101109137851423
7149131510120116582314
8151391412101105673241
9274581630111014151213
1034761852110915141312
1145612387109013121514
1261834725141513011910
1358127436151412110109
1476583214121315910011
1583276541131214109110

Centre:   0   14

Centrum:   0   14

Nucleus:   0   14

Left Nucleus:   0   14

Middle Nucleus:   0   14

Right Nucleus:   0   14


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   4   6   7   8   9   10   11   12   13   14   15

2 Elements of order 4:   3   5

Commutator Subloop:   0   14

Associator Subloop:   0   14

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(9,12) 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