Right Bol Loop 16.3.4.10 of order 16

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

Centre: 0 2

Centrum: 0 2 4 6

Nucleus: 0 2

Left Nucleus: 0 2 4 6

Middle Nucleus: 0 2

Right Nucleus: 0 2

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

3 Elements of order 2: 2 4 6

12 Elements of order 4: 1 3 5 7 8 9 10 11 12 13 14 15

Commutator Subloop: 0 2 4 6

Associator Subloop: 0 2 4 6

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 5 7
8 11 14 15
9 10 12 13

Automorphic Inverse Property: HOLDS

A_l Property: FAILS. The left inner mapping L_1,8 = (4,6)(5,7)(8,15)(9,13)(10,12)(11,14) is not an automorphism. L_1,8(4*8) neq L_1,8(4)*L_1,8(8)

A_r Property: HOLDS (i.e. every right inner mapping R_a,b is an automorphism)

Right (Left, Full) Mult Group Orders: 64 (1024, 4096)

/ revised October, 2001

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

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

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