Right Bol Loop 16.13.2.12 of order 16

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

Centre: 0 14

Centrum: 0 14

Nucleus: 0 14

Left Nucleus: 0 11 13 14

Middle Nucleus: 0 14

Right Nucleus: 0 14

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 3 4 5 7 8 9 10 11 12 13 14 15

2 Elements of order 4: 2 6

Commutator Subloop: 0 14

Associator Subloop: 0 14

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

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

A_l Property: FAILS. The left inner mapping L_1,1 = (4,5)(11,13) 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: 64 (1024, 2048)

/ revised October, 2001

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

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

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