Right Bol Loop 16.5.2.12 of order 16


0123456789101112131415
1250367498141315101112
2561074314119121081513
3014725611141581391210
4307612513101291115814
5672143010138151412911
6745230115121110914138
7436501212151314811109
8101312149151167531240
9151113101412876240351
1013981215111432064175
1114121598101354602713
1281014111391510426537
1391510811141223715064
1412811151013945173602
1511149131281001357426

Centre:   0   6

Centrum:   0   6

Nucleus:   0   6

Left Nucleus:   0   6   10   11

Middle Nucleus:   0   6

Right Nucleus:   0   6


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:   6   10   11   13   14

6 Elements of order 4:   2   4   8   9   12   15

4 Elements of order 8:   1   3   5   7

Commutator Subloop:   0   2   4   6

Associator Subloop:   0   2   4   6

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 L1,1 = (8,13)(9,10)(11,12)(14,15) is not an automorphism.   L1,1(1*9) neq L1,1(1)*L1,1(9)

Ar Property:   FAILS. The right inner mapping R1,8 = (1,3)(2,4)(5,7)(8,13)(9,12)(14,15) is not an automorphism.   R1,8(1*8) neq R1,8(1)*R1,8(8)

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


/ revised October, 2001