Right Bol Loop 16.9.2.33 of order 16

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

Centre: 0 12

Centrum: 0 12

Nucleus: 0 12

Left Nucleus: 0 10 12 14

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

9 Elements of order 2: 3 6 9 10 11 12 13 14 15

6 Elements of order 4: 1 2 4 5 7 8

Commutator Subloop: 0 12

Associator Subloop: 0 12

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Automorphic Inverse Property: FAILS. (1^-1)(4^-1) neq (1*4)^-1

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