Right Bol Loop 16.1.2.2 of order 16

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

Centre: 0 6

Centrum: 0 6

Nucleus: 0 6

Left Nucleus: 0 6 8 15

Middle Nucleus: 0 6

Right Nucleus: 0 6

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

1 Element of order 2: 6

6 Elements of order 4: 2 4 8 11 13 15

8 Elements of order 8: 1 3 5 7 9 10 12 14

Commutator Subloop: 0 2 4 6

Associator Subloop: 0 2 4 6

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 5 7
8 11 13 15
9 10 12 14

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

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

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

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

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

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