Right Bol Loop 16.9.2.343 of order 16

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

6 Elements of order 4: 1 2 6 7 11 12

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