Right Bol Loop 16.11.4.39 of order 16


0123456789101112131415
1032547691581413111210
2406173511131415810912
3517062413121191015814
4260715314111210981513
5371604212141381591011
6745230110815131412119
7654321015109121114138
8101213141191506152347
9151411121381010734256
1081312111415967043521
1113151098141224307615
1214891015131153470162
1311101589121432561704
1412981510111345216073
1591114131210871625430

Centre:   0   7

Centrum:   0   7   13   14

Nucleus:   0   3   4   7

Left Nucleus:   0   3   4   7   8   13   14   15

Middle Nucleus:   0   3   4   7

Right Nucleus:   0   3   4   7


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

11 Elements of order 2:   1   2   5   6   7   8   9   10   11   12   15

4 Elements of order 4:   3   4   13   14

Commutator Subloop:   0   7

Associator Subloop:   0   7

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:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   32 (64, 128)


/ revised October, 2001