Right Bol Loop 16.1.2.27 of order 16


0123456789101112131415
1032547698111013121514
2310674510118914151312
3201765411109815141213
4567103212131514981011
5476012313121415891110
6754321015141213101189
7645230114151312111098
8910111312141510324576
9811101213151401235467
1011981415131232107654
1110891514121323016745
1213151489101154761023
1312141598111045670132
1415121311109867453210
1514131210118976542301

Centre:   0   1

Centrum:   0   1

Nucleus:   0   1

Left Nucleus:   0   1   4   5   8   9   12   13

Middle Nucleus:   0   1   14   15

Right Nucleus:   0   1   14   15


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

1 Element of order 2:   1

14 Elements of order 4:   2   3   4   5   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   1

Associator Subloop:   0   1

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(5-1) neq (2*5)-1

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

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

Right (Left, Full) Mult Group Orders:   32 (64, 256)


/ revised October, 2001