Right Bol Loop 16.3.2.109 of order 16

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

Centre: 0 2

Centrum: 0 2

Nucleus: 0 2

Left Nucleus: 0 2 6 7

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 6 7

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

Commutator Subloop: 0 2 6 7

Associator Subloop: 0 2 6 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 4 5
8 11 14 15
9 10 12 13

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

A_l Property: FAILS. The left inner mapping L_1,8 = (4,5)(6,7)(8,15)(9,12)(10,13)(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 (4096, 16384)

/ revised October, 2001

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

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

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