Right Bol Loop 16.13.2.1 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	14	12	10	15	8	13	11
2	4	0	6	1	7	3	5	10	12	8	13	9	11	15	14
3	5	1	7	0	6	2	4	11	10	13	14	8	15	12	9
4	2	6	0	7	1	5	3	12	15	9	8	14	10	11	13
5	3	7	1	6	0	4	2	15	11	14	9	13	12	10	8
6	7	4	5	2	3	0	1	13	8	11	15	10	14	9	12
7	6	5	4	3	2	1	0	14	13	15	12	11	9	8	10
8	10	9	11	12	13	15	14	0	6	2	4	3	1	7	5
9	11	8	10	15	14	12	13	1	0	4	5	2	7	6	3
10	8	12	13	9	11	14	15	2	3	0	1	6	4	5	7
11	9	15	14	8	10	13	12	3	5	6	0	7	2	4	1
12	13	10	8	14	15	9	11	4	2	1	7	0	5	3	6
13	12	14	15	10	8	11	9	6	7	3	2	5	0	1	4
14	15	13	12	11	9	10	8	7	1	5	3	4	6	0	2
15	14	11	9	13	12	8	10	5	4	7	6	1	3	2	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

13 Elements of order 2: 1 2 5 6 7 8 9 10 11 12 13 14 15

2 Elements of order 4: 3 4

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 11 12 14
9 10 13 15

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