Right Bol Loop 16.7.2.398 of order 16


0123456789101112131415
1230547698111013151214
2301765411109815141312
3012674510118914121513
4675031212131415891011
5467120314151213108119
6754302113121514911810
7546213015141312111098
8101191514131223104567
9810111312151432016475
1011981415121310235746
1198101213141501327654
1214151311109875640312
1312141598111057461023
1415131210118964753201
1513121489101146572130

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   4   7

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   12   13   14   15

8 Elements of order 4:   1   3   5   6   8   9   10   11

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

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:   64 (1024, 2048)


/ revised October, 2001