Right Bol Loop 16.13.2.50 of order 16

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

Centre: 0 13

Centrum: 0 13

Nucleus: 0 13

Left Nucleus: 0 11 13 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

13 Elements of order 2: 1 3 4 5 6 7 9 10 11 12 13 14 15

2 Elements of order 4: 2 8

Commutator Subloop: 0 13

Associator Subloop: 0 13

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

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

A_l Property: FAILS. The left inner mapping L_1,1 = (4,6)(11,15) 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: 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	12	11	10	15	13	14	2	5	6	3	7	8	4
2	9	13	11	10	15	12	14	0	1	6	5	4	8	7	3
3	10	15	0	9	13	14	12	11	4	7	8	1	5	6	2
4	11	10	14	0	9	13	15	12	3	8	7	2	6	5	1
5	12	11	13	14	0	9	10	15	6	1	2	7	3	4	8
6	15	12	9	13	14	0	11	10	5	2	1	8	4	3	7
7	13	14	10	15	12	11	0	9	8	3	4	5	1	2	6
8	14	0	15	12	11	10	9	13	7	4	3	6	2	1	5
9	2	7	6	3	4	5	8	1	0	11	10	15	14	13	12
10	3	6	7	2	1	8	5	4	11	0	9	13	12	15	14
11	4	3	2	1	8	7	6	5	10	9	0	14	15	12	13
12	5	4	1	8	7	2	3	6	15	13	14	0	10	11	9
13	7	8	5	6	3	4	1	2	14	12	15	10	0	9	11
14	8	1	4	5	6	3	2	7	13	15	12	11	9	0	10
15	6	5	8	7	2	1	4	3	12	14	13	9	11	10	0

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

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