Right Bol Loop 16.7.2.96 of order 16

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	5	7	4	6	9	11	8	10	13	12	15	14
2	3	0	1	6	4	7	5	10	8	11	9	14	15	12	13
3	2	1	0	7	6	5	4	11	10	9	8	15	14	13	12
4	6	5	7	0	2	1	3	12	14	13	15	8	10	9	11
5	7	4	6	1	0	3	2	13	12	15	14	9	11	8	10
6	4	7	5	2	3	0	1	14	15	12	13	10	8	11	9
7	5	6	4	3	1	2	0	15	13	14	12	11	9	10	8
8	9	10	11	15	13	14	12	3	1	2	0	7	5	6	4
9	8	11	10	14	15	12	13	2	3	0	1	6	4	7	5
10	11	8	9	13	12	15	14	1	0	3	2	5	7	4	6
11	10	9	8	12	14	13	15	0	2	1	3	4	6	5	7
12	14	13	15	11	10	9	8	7	6	5	4	3	2	1	0
13	15	12	14	10	8	11	9	6	4	7	5	2	3	0	1
14	12	15	13	9	11	8	10	5	7	4	6	1	0	3	2
15	13	14	12	8	9	10	11	4	5	6	7	0	1	2	3

Centre: 0 3

Centrum: 0 3

Nucleus: 0 3

Left Nucleus: 0 3 4 7

Middle Nucleus: 0 3

Right Nucleus: 0 3

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: 1 2 3 4 5 6 7

8 Elements of order 4: 8 9 10 11 12 13 14 15

Commutator Subloop: 0 3

Associator Subloop: 0 3

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

1 2
4 7
5 6
8 11
9 10
12 15
13 14

Automorphic Inverse Property: HOLDS

A_l Property: FAILS. The left inner mapping L_1,8 = (4,7)(5,6)(8,11)(9,10)(12,15)(13,14) is not an automorphism. L_1,8(4*8) neq L_1,8(4)*L_1,8(8)

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

Right (Left, Full) Mult Group Orders: 64 (1024, 2048)

/ revised October, 2001

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	5	7	4	6	9	11	8	10	13	12	15	14
2	3	0	1	6	4	7	5	10	8	11	9	14	15	12	13
3	2	1	0	7	6	5	4	11	10	9	8	15	14	13	12
4	6	5	7	0	2	1	3	12	14	13	15	8	10	9	11
5	7	4	6	1	0	3	2	13	12	15	14	9	11	8	10
6	4	7	5	2	3	0	1	14	15	12	13	10	8	11	9
7	5	6	4	3	1	2	0	15	13	14	12	11	9	10	8
8	9	10	11	15	13	14	12	3	1	2	0	7	5	6	4
9	8	11	10	14	15	12	13	2	3	0	1	6	4	7	5
10	11	8	9	13	12	15	14	1	0	3	2	5	7	4	6
11	10	9	8	12	14	13	15	0	2	1	3	4	6	5	7
12	14	13	15	11	10	9	8	7	6	5	4	3	2	1	0
13	15	12	14	10	8	11	9	6	4	7	5	2	3	0	1
14	12	15	13	9	11	8	10	5	7	4	6	1	0	3	2
15	13	14	12	8	9	10	11	4	5	6	7	0	1	2	3

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	5	7	4	6	9	11	8	10	13	12	15	14
2	3	0	1	6	4	7	5	10	8	11	9	14	15	12	13
3	2	1	0	7	6	5	4	11	10	9	8	15	14	13	12
4	6	5	7	0	2	1	3	12	14	13	15	8	10	9	11
5	7	4	6	1	0	3	2	13	12	15	14	9	11	8	10
6	4	7	5	2	3	0	1	14	15	12	13	10	8	11	9
7	5	6	4	3	1	2	0	15	13	14	12	11	9	10	8
8	9	10	11	15	13	14	12	3	1	2	0	7	5	6	4
9	8	11	10	14	15	12	13	2	3	0	1	6	4	7	5
10	11	8	9	13	12	15	14	1	0	3	2	5	7	4	6
11	10	9	8	12	14	13	15	0	2	1	3	4	6	5	7
12	14	13	15	11	10	9	8	7	6	5	4	3	2	1	0
13	15	12	14	10	8	11	9	6	4	7	5	2	3	0	1
14	12	15	13	9	11	8	10	5	7	4	6	1	0	3	2
15	13	14	12	8	9	10	11	4	5	6	7	0	1	2	3

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	5	7	4	6	9	11	8	10	13	12	15	14
2	3	0	1	6	4	7	5	10	8	11	9	14	15	12	13
3	2	1	0	7	6	5	4	11	10	9	8	15	14	13	12
4	6	5	7	0	2	1	3	12	14	13	15	8	10	9	11
5	7	4	6	1	0	3	2	13	12	15	14	9	11	8	10
6	4	7	5	2	3	0	1	14	15	12	13	10	8	11	9
7	5	6	4	3	1	2	0	15	13	14	12	11	9	10	8
8	9	10	11	15	13	14	12	3	1	2	0	7	5	6	4
9	8	11	10	14	15	12	13	2	3	0	1	6	4	7	5
10	11	8	9	13	12	15	14	1	0	3	2	5	7	4	6
11	10	9	8	12	14	13	15	0	2	1	3	4	6	5	7
12	14	13	15	11	10	9	8	7	6	5	4	3	2	1	0
13	15	12	14	10	8	11	9	6	4	7	5	2	3	0	1
14	12	15	13	9	11	8	10	5	7	4	6	1	0	3	2
15	13	14	12	8	9	10	11	4	5	6	7	0	1	2	3