Right Bol Loop 16.7.2.4 of order 16


0123456789101112131415
1032765498111015141312
2301547610119814121513
3210674511108913151214
4756023115121314910118
5647201313141215119810
6574310214131512108911
7465132012151413811109
8121314151011947651320
9151413121110874560231
1014151213891156473012
1113121514981065742103
1281110914131510234567
1311891015121423016475
1410981112151332105746
1591011813141201327654

Centre:   0   4

Centrum:   0   4

Nucleus:   0   4

Left Nucleus:   0   1   4   7

Middle Nucleus:   0   4

Right Nucleus:   0   4


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

7 Elements of order 2:   1   2   3   4   5   6   7

8 Elements of order 4:   8   9   10   11   12   13   14   15

Commutator Subloop:   0   1   4   7

Associator Subloop:   0   1   4   7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (2,5)(3,6)(8,15)(9,12)(10,13)(11,14) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

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

Right (Left, Full) Mult Group Orders:   64 (4096, 16384)


/ revised October, 2001