Right Bol Loop 16.15.2.6 of order 16


0123456789101112131415
1032547698111015141312
2301675410118914121513
3210764511109813151214
4576013212151314810119
5467102315121413911108
6754230113141215118910
7645321014131512109811
8911101215131401234675
9810111512141310325764
1011981314151223017456
1110891413121532106547
1215131489111045670231
1314121510118967453012
1413151211109876542103
1512141398101154761320

Centre:   0   1

Centrum:   0   1

Nucleus:   0   1

Left Nucleus:   0   1

Middle Nucleus:   0   1

Right Nucleus:   0   1


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

15 Elements of order 2:   1   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:   HOLDS

Al Property:   FAILS. The left inner mapping L2,8 = (4,5)(6,7)(8,9)(10,11)(12,15)(13,14) is not an automorphism.   L2,8(4*8) neq L2,8(4)*L2,8(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