Right Bol Loop 16.9.4.5 of order 16

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

Centre: 0 13

Centrum: 0 10 13 15

Nucleus: 0 13

Left Nucleus: 0 9 10 11 12 13 14 15

Middle Nucleus: 0 13

Right Nucleus: 0 13

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 8 9 10 11 12 13 14 15

6 Elements of order 4: 2 3 4 5 6 7

Commutator Subloop: 0 13

Associator Subloop: 0 13

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

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

A_l Property: FAILS. The left inner mapping L_1,1 = (3,7)(10,15) is not an automorphism. L_1,1(2*3) neq L_1,1(2)*L_1,1(3)

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

Right (Left, Full) Mult Group Orders: 32 (1024, 2048)

/ revised October, 2001

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

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

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