Right Bol Loop 16.9.2.112 of order 16

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

Centre: 0 15

Centrum: 0 15

Nucleus: 0 15

Left Nucleus: 0 10 13 15

Middle Nucleus: 0 15

Right Nucleus: 0 15

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 8 9 10 11 12 13 14 15

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

Commutator Subloop: 0 15

Associator Subloop: 0 15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

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

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

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

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