Right Bol Loop 16.9.2.421 of order 16


0123456789101112131415
1032547698141315111012
2406173511131281091514
3517062412151110814139
4260715313111591481210
5371604215121314910118
6745230110148121115913
7654321014109151312811
8101113121591471624305
9141215111381060742513
1081311151214917035264
1112891014131554301627
1211981410151345267031
1315101489111232510746
1491512131110806153472
1513141098121123476150

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   2   5   7   9   10   12   13

Middle Nucleus:   0   1   6   7

Right Nucleus:   0   1   6   7


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

9 Elements of order 2:   1   2   5   6   7   9   10   11   15

6 Elements of order 4:   3   4   8   12   13   14

Commutator Subloop:   0   7

Associator Subloop:   0   7

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-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