Right Bol Loop 16.5.2.3 of order 16

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

Centre: 0 6

Centrum: 0 6

Nucleus: 0 6

Left Nucleus: 0 6 10 12

Middle Nucleus: 0 6

Right Nucleus: 0 6

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

5 Elements of order 2: 6 9 10 12 15

2 Elements of order 4: 2 4

8 Elements of order 8: 1 3 5 7 8 11 13 14

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 13 14
9 10 12 15

Automorphic Inverse Property: FAILS. (1^-1)(9^-1) neq (1*9)^-1

A_l Property: FAILS. The left inner mapping L_1,1 = (8,11)(9,12)(10,15)(13,14) is not an automorphism. L_1,1(1*8) neq L_1,1(1)*L_1,1(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	5	0	3	6	7	4	9	8	13	10	11	12	15	14
2	5	6	1	0	7	4	3	13	10	15	8	9	14	11	12
3	0	1	4	7	2	5	6	10	13	14	15	8	9	12	11
4	3	0	7	6	1	2	5	11	12	9	14	15	8	13	10
5	6	7	2	1	4	3	0	12	11	8	9	14	15	10	13
6	7	4	5	2	3	0	1	14	15	12	13	10	11	8	9
7	4	3	6	5	0	1	2	15	14	11	12	13	10	9	8
8	9	13	10	11	12	14	15	2	1	5	0	3	6	4	7
9	13	12	8	10	14	15	11	5	0	4	1	2	7	3	6
10	8	9	11	15	13	12	14	1	2	0	3	6	5	7	4
11	10	8	15	14	9	13	12	0	5	7	4	1	2	6	3
12	14	15	13	9	11	10	8	7	4	6	5	0	3	1	2
13	12	14	9	8	15	11	10	6	3	1	2	7	4	0	5
14	15	11	12	13	10	8	9	4	7	3	6	5	0	2	1
15	11	10	14	12	8	9	13	3	6	2	7	4	1	5	0

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

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