Right Bol Loop 16.3.2.9 of order 16

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

Centre: 0 7

Centrum: 0 7

Nucleus: 0 7

Left Nucleus: 0 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

3 Elements of order 2: 7 10 12

8 Elements of order 4: 2 4 8 9 11 13 14 15

4 Elements of order 8: 1 3 5 6

Commutator Subloop: 0 2 4 7

Associator Subloop: 0 2 4 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 5 6
8 11 13 14
9 10 12 15

Automorphic Inverse Property: FAILS. (1^-1)(9^-1) neq (1*9)^-1

A_l Property: FAILS. The left inner mapping L_1,1 = (8,11)(9,12)(10,15)(13,14) is not an automorphism. L_1,1(1*9) neq L_1,1(1)*L_1,1(9)

A_r Property: FAILS. The right inner mapping R_1,8 = (1,3)(2,4)(5,6)(8,11)(9,15)(13,14) is not an automorphism. R_1,8(1*8) neq R_1,8(1)*R_1,8(8)

Right (Left, Full) Mult Group Orders: 64 (4096, 16384)

/ revised October, 2001

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

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

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