Right Bol Loop 16.13.4.0 of order 16

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

Centre: 0 14

Centrum: 0 10 14 15

Nucleus: 0 14

Left Nucleus: 0 9 10 11 12 13 14 15

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 3 5 7 8 9 10 11 12 13 14 15

2 Elements of order 4: 4 6

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 12
10 15
11 13

Automorphic Inverse Property: FAILS. (1^-1)(5^-1) neq (1*5)^-1

A_l Property: FAILS. The left inner mapping L_1,1 = (2,5)(9,12) 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: 32 (1024, 2048)

/ revised October, 2001

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

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

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