Right Bol Loop 16.13.2.18 of order 16

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

Centre: 0 14

Centrum: 0 14

Nucleus: 0 14

Left Nucleus: 0 9 13 14

Middle Nucleus: 0 14

Right Nucleus: 0 14

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

13 Elements of order 2: 1 2 4 5 6 8 9 10 11 12 13 14 15

2 Elements of order 4: 3 7

Commutator Subloop: 0 14

Associator Subloop: 0 14

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

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

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