Right Bol Loop 16.9.2.2 of order 16

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

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 2 5 7

Middle Nucleus: 0 7

Right Nucleus: 0 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 8 13 14 15

6 Elements of order 4: 3 4 9 10 11 12

Commutator Subloop: 0 3 4 7

Associator Subloop: 0 3 4 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

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

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

A_l Property: FAILS. The left inner mapping L_1,8 = (2,5)(3,4)(8,14,15,13)(9,10,12,11) is not an automorphism. L_1,8(2*8) neq L_1,8(2)*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, 4096)

/ revised October, 2001

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

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

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