Right Bol Loop 16.7.2.351 of order 16


0123456789101112131415
1230547691181013121514
2301765411109815141312
3012674510811914151213
4576031212141315891011
5764120314151213101189
6457302113121514981110
7645213015131412111098
8101191514131223107654
9810111312151430215476
1011981415121312036745
1198101213141501324567
1213151411109876542130
1315141298111057463021
1412131510118964751203
1514121389101145670312

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

7 Elements of order 2:   2   4   7   9   10   13   14

8 Elements of order 4:   1   3   5   6   8   11   12   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (8,11)(9,10) 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