Right Bol Loop 16.11.2.123 of order 16


0123456789101112131415
1230574698111013121514
2301765411109815141312
3012647510118914151213
4675031212131415111098
5467102313121514101189
6754320114151213981110
7546213015141312891011
8101191214131521307654
9810111312151430216745
1011981415121312035476
1198101513141203124567
1213151489101175640132
1315141291181064751023
1412131510811957463201
1514121311109846572310

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

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

11 Elements of order 2:   2   4   5   6   7   9   10   12   13   14   15

4 Elements of order 4:   1   3   8   11

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,8 = (12,15)(13,14) 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:   128 (1024, 2048)


/ revised October, 2001