Right Bol Loop 16.3.2.110 of order 16


0123456789101112131415
1230764591181015141213
2301547611109813121514
3012675410811914151312
4756201312151413118910
5647023113141512811109
6475130214121315910811
7564312015131214109118
8121113910151421304576
9151014118131232017654
1014915811121310236745
1113812109141503125467
1211138151410957642031
1381211141591046750213
1491510121311874561320
1510149131281165473102

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3   4   5   6   7

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

3 Elements of order 2:   2   6   7

12 Elements of order 4:   1   3   4   5   8   9   10   11   12   13   14   15

Commutator Subloop:   0   2   6   7

Associator Subloop:   0   2   6   7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,5)(6,7)(8,15)(9,13)(10,12)(11,14) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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

Right (Left, Full) Mult Group Orders:   64 (1024, 4096)


/ revised October, 2001