Right Bol Loop 16.5.2.287 of order 16


0123456789101112131415
1901011121514132437685
2091110131415121346758
3111090151312144125876
4101109141213153218567
5131215149111008673421
6151412131090117852143
7141513121109106581234
8121314150101195764312
9214387650111013121514
1034217586119014151312
1143126857100915141213
1258762341131514091110
1385671432121415901011
1467583124151213101109
1576854213141312111090

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9   14   15

Middle Nucleus:   0   9   10   11

Right Nucleus:   0   9   10   11


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

5 Elements of order 2:   9   12   13   14   15

10 Elements of order 4:   1   2   3   4   5   6   7   8   10   11

Commutator Subloop:   0   9   10   11

Associator Subloop:   0   9   10   11

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

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

Al Property:   FAILS. The left inner mapping L1,1 = (5,6,8,7)(12,15,13,14) is not an automorphism.   L1,1(5*1) neq L1,1(5)*L1,1(1)

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

Right (Left, Full) Mult Group Orders:   32 (512, 2048)


/ revised October, 2001