Right Bol Loop 16.5.4.14 of order 16

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

Centre: 0 12

Centrum: 0 9 12 15

Nucleus: 0 12

Left Nucleus: 0 9 10 11 12 13 14 15

Middle Nucleus: 0 12

Right Nucleus: 0 12

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

5 Elements of order 2: 1 8 9 12 15

10 Elements of order 4: 2 3 4 5 6 7 10 11 13 14

Commutator Subloop: 0 9 12 15

Associator Subloop: 0 9 12 15

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

9 15

3 Conjugacy Classes of size 4:

1 2 7 8
3 4 5 6
10 11 13 14

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

A_l Property: FAILS. The left inner mapping L_1,1 = (2,7)(3,5)(4,6)(9,15)(10,13)(11,14) is not an automorphism. L_1,1(2*3) neq L_1,1(2)*L_1,1(3)

A_r Property: FAILS. The right inner mapping R_1,3 = (1,7)(2,8)(3,5)(4,6) is not an automorphism. R_1,3(1*1) neq R_1,3(1)*R_1,3(1)

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