Cebirde **sonlu alan** veya **Galois alanı** (Évariste Galois'e ithaf edilsin diye bu adla adlandırıldı), sonlu sayıda elemandan oluşan bir cisimdir. Herhangi bir alan olarak düşünülürse sonlu alan, değişme, çarpma, toplama, çıkarma ve (sıfırdan farklı) bölme işlemlerinin tanımlandığı bir kümedir. Sonlu alanlara yaygın örnek, ℤ/3ℤ veya ℤ/7ℤ gibi tam sayı olan **asal tam sayılar modülü** verilebilir.

Sonlu alanlar yalnızca, (*p* bir asal sayı ve *k* pozitif tam sayı olan) *pk* asal kuvveti için geçerlidir. Her bir asal kuvvet için bu boyuta sahip tek sonlu alan vardır. Bu boyuttaki tüm alanlar izomorfiktir. *pk* boyutuna sahip bir alanın karakteristiği *p* dir. Bu, sonuç sıfır olana kadar her elemanın kopyalanarak *p*ye eklenmesi anlamına gelir. Örneğin; ℤ/2ℤ (tam sayı mod 2), 1 + 1 = 0 olduğunda karakteristiği 2 olur. ℤ/5ℤ, 0 = 1 + 1 + 1 + 1 + 1 = 2 + 2 + 2 + 2 + 2 = vb. olduğunda karakteristiği 5 olur.

*q* kuvvetine sahip bir sonlu alanda *Xq* − *X* polinomunun tüm ögeleri, onun kökleri olur. Böylece *q* farklı doğrusal faktörleri elde edilir.

Sonlu alanlara, sayılar teorisi, cebirsel geometri, Galois teorisi, sonlu geometri, kriptografi ve kodlama kuramı da dahil matematik ve bilgisayar biliminde çok sık rastlanır.

Bazı küçük sonlu alanlar
------------------------

### F2

|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 

| + | 0 | 1 |
| --- | --- | --- |
| 0 | 0 | 1 |
| 1 | 1 | 0 |

 | 

| × | 0 | 1 |
| --- | --- | --- |
| 0 | 0 | 0 |
| 1 | 0 | 1 |

 |

### F3

|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 

| + | 0 | 1 | 2 |
| --- | --- | --- | --- |
| 0 | 0 | 1 | 2 |
| 1 | 1 | 2 | 0 |
| 2 | 2 | 0 | 1 |

 | 

| × | 0 | 1 | 2 |
| --- | --- | --- | --- |
| 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 |
| 2 | 0 | 2 | 1 |

 |

### F4

|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 

| + | 0 | 1 | α | α+1 |
| --- | --- | --- | --- | --- |
| 0 | 0 | 1 | α | α+1 |
| 1 | 1 | 0 | α+1 | α |
| α | α | α+1 | 0 | 1 |
| α+1 | α+1 | α | 1 | 0 |

 | 

| × | 0 | 1 | α | α+1 |
| --- | --- | --- | --- | --- |
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | α | α+1 |
| α | 0 | α | α+1 | 1 |
| α+1 | 0 | α+1 | 1 | α |

 |

### F8

```
Matris tam sayıları modül 2'yi ifade eden sekiz ögeli alan

  öge (0)         öge (1)         öge (2)         öge (3)

  0  0  0         1  0  0         0  1  0         0  0  1
  0  0  0         0  1  0         0  0  1         1  1  0
  0  0  0         0  0  1         1  1  0         0  1  1

  öge (4)         öge (5)         öge (6)         öge (7)

  1  1  0         0  1  1         1  1  1         1  0  1
  0  1  1         1  1  1         1  0  1         1  0  0
  1  1  1         1  0  1         1  0  0         0  1  0

+/  (0) (1) (2) (3) (4) (5) (6) (7)
(0)  0   1   2   3   4   5   6   7
(1)  1   0   4   7   2   6   5   3
(2)  2   4   0   5   1   3   7   6
(3)  3   7   5   0   6   2   4   1
(4)  4   2   1   6   0   7   3   5
(5)  5   6   3   2   7   0   1   4
(6)  6   5   7   4   3   1   0   2
(7)  7   3   6   1   5   4   2   0

x/  (0) (1) (2) (3) (4) (5) (6) (7)
(0)  0   0   0   0   0   0   0   0
(1)  0   1   2   3   4   5   6   7
(2)  0   2   3   4   5   6   7   1
(3)  0   3   4   5   6   7   1   2
(4)  0   4   5   6   7   1   2   3
(5)  0   5   6   7   1   2   3   4
(6)  0   6   7   1   2   3   4   5
(7)  0   7   1   2   3   4   5   6

```

### F9

```
Matris tam sayıları modül 3'ü ifade eden 9 ögeli alan

 öge (0)         öge (1)        öge (2)

  0  0            1  0            0  1
  0  0            0  1            1  1

 öge (3)         öge (4)        öge (5)

  1  1            1  2            2  0
  1  2            2  0            0  2

 öge (6)         öge (7)        öge (8)

  0  2            2  2            2  1
  2  2            2  1            1  0

+/  (0) (1) (2) (3) (4) (5) (6) (7) (8)
(0)  0   1   2   3   4   5   6   7   8
(1)  1   5   3   8   7   0   4   6   2
(2)  2   3   6   4   1   8   0   5   7
(3)  3   8   4   7   5   2   1   0   6
(4)  4   7   1   5   8   6   3   2   0
(5)  5   0   8   2   6   1   7   4   3
(6)  6   4   0   1   3   7   2   8   5
(7)  7   6   5   0   2   4   8   3   1
(8)  8   2   7   6   0   3   5   1   4

x/  (0) (1) (2) (3) (4) (5) (6) (7) (8)
(0)  0   0   0   0   0   0   0   0   0
(1)  0   1   2   3   4   5   6   7   8
(2)  0   2   3   4   5   6   7   8   1
(3)  0   3   4   5   6   7   8   1   2
(4)  0   4   5   6   7   8   1   2   3
(5)  0   5   6   7   8   1   2   3   4
(6)  0   6   7   8   1   2   3   4   5
(7)  0   7   8   1   2   3   4   5   6
(8)  0   8   1   2   3   4   5   6   7

```

### F16

**F**16,
**a + b x + c x**2**+ d x**3 polinomu ile ifade edilir.  

**a**, **b**, **c** ve **d** tam sayı modül **2** dir.  

Polinomlar, **x**4**= 1 + x** kuralı kullanılarak **x** kuvvetleri ile elde edilir.

. 

```
ö ( 0)        ö ( 1)        ö ( 2)        ö ( 3)
[ 0  0  0  0] [ 1  0  0  0] [ 0  1  0  0] [ 0  0  1  0]

ö ( 4)        ö ( 5)        ö ( 6)        ö ( 7)
[ 0  0  0  1] [ 1  1  0  0] [ 0  1  1  0] [ 0  0  1  1]

ö ( 8)        ö ( 9)        ö (10)        ö (11)
[ 1  1  0  1] [ 1  0  1  0] [ 0  1  0  1] [ 1  1  1  0]

ö (12)        ö (13)        ö (14)        ö (15)
[ 0  1  1  1] [ 1  1  1  1] [ 1  0  1  1] [ 1  0  0  1]

+/   0_ 1_ 2_ 3_ 4_ 5_ 6_ 7_ 8_ 9_10_11_12_13_14_15_
 0_  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
 1_  1  0  5  9 15  2 11 14 10  3  8  6 13 12  7  4
 2_  2  5  0  6 10  1  3 12 15 11  4  9  7 14 13  8
 3_  3  9  6  0  7 11  2  4 13  1 12  5 10  8 15 14
 4_  4 15 10  7  0  8 12  3  5 14  2 13  6 11  9  1
 5_  5  2  1 11  8  0  9 13  4  6 15  3 14  7 12 10
 6_  6 11  3  2 12  9  0 10 14  5  7  1  4 15  8 13
 7_  7 14 12  4  3 13 10  0 11 15  6  8  2  5  1  9
 8_  8 10 15 13  5  4 14 11  0 12  1  7  9  3  6  2
 9_  9  3 11  1 14  6  5 15 12  0 13  2  8 10  4  7
10_ 10  8  4 12  2 15  7  6  1 13  0 14  3  9 11  5
11_ 11  6  9  5 13  3  1  8  7  2 14  0 15  4 10 12
12_ 12 13  7 10  6 14  4  2  9  8  3 15  0  1  5 11
13_ 13 12 14  8 11  7 15  5  3 10  9  4  1  0  2  6
14_ 14  7 13 15  9 12  8  1  6  4 11 10  5  2  0  3
15_ 15  4  8 14  1 10 13  9  2  7  5 12 11  6  3  0

x/   0_ 1_ 2_ 3_ 4_ 5_ 6_ 7_ 8_ 9_10_11_12_13_14_15_
 0_  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 1_  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
 2_  0  2  3  4  5  6  7  8  9 10 11 12 13 14 15  1
 3_  0  3  4  5  6  7  8  9 10 11 12 13 14 15  1  2
 4_  0  4  5  6  7  8  9 10 11 12 13 14 15  1  2  3
 5_  0  5  6  7  8  9 10 11 12 13 14 15  1  2  3  4
 6_  0  6  7  8  9 10 11 12 13 14 15  1  2  3  4  5
 7_  0  7  8  9 10 11 12 13 14 15  1  2  3  4  5  6
 8_  0  8  9 10 11 12 13 14 15  1  2  3  4  5  6  7
 9_  0  9 10 11 12 13 14 15  1  2  3  4  5  6  7  8
10_  0 10 11 12 13 14 15  1  2  3  4  5  6  7  8  9
11_  0 11 12 13 14 15  1  2  3  4  5  6  7  8  9 10
12_  0 12 13 14 15  1  2  3  4  5  6  7  8  9 10 11
13_  0 13 14 15  1  2  3  4  5  6  7  8  9 10 11 12
14_  0 14 15  1  2  3  4  5  6  7  8  9 10 11 12 13
15_  0 15  1  2  3  4  5  6  7  8  9 10 11 12 13 14

```

### F25

**F**25, **a + b√2** sayıları ile ifade edilir.
**a** ve **b**, tam sayı modül **5** dir.  

**2 + √2** kuvvetleri ile elde edilir.

|  |  |  |  |  |
| --- | --- | --- | --- | --- |
| ö (0) | ö (1) | ö (2) | ö (3) | ö (4) |
| 0 + 0√2 | 1 + 0√2 | 2 + 1√2 | 1 + 4√2 | 0 + 4√2 |
| ö (5) | ö (6) | ö (7) | ö (8) | ö (9) |
| 3 + 3√2 | 2 + 4√2 | 2 + 0√2 | 4 + 2√2 | 2 + 3√2 |
| ö (10) | ö (11) | ö (12) | ö (13) | ö (14) |
| 0 + 3√2 | 1 + 1√2 | 4 + 3√2 | 4 + 0√2 | 3 + 4√2 |
| ö (15) | ö (16) | ö (17) | ö (18) | ö (19) |
| 4 + 1√2 | 0 + 1√2 | 2 + 2√2 | 3 + 1√2 | 3 + 0√2 |
| ö (20) | ö (21) | ö (22) | ö (23) | ö (24) |
| 1 + 3√2 | 3 + 2√2 | 0 + 2√2 | 4 + 4√2 | 1 + 2√2 |

| + | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| 1 | 1 | 7 | 18 | 6 | 3 | 12 | 14 | 19 | 22 | 5 | 20 | 2 | 10 | 0 | 23 | 16 | 11 | 21 | 15 | 13 | 9 | 8 | 24 | 4 | 17 |
| 2 | 2 | 18 | 8 | 19 | 7 | 4 | 13 | 15 | 20 | 23 | 6 | 21 | 3 | 11 | 0 | 24 | 17 | 12 | 22 | 16 | 14 | 10 | 9 | 1 | 5 |
| 3 | 3 | 6 | 19 | 9 | 20 | 8 | 5 | 14 | 16 | 21 | 24 | 7 | 22 | 4 | 12 | 0 | 1 | 18 | 13 | 23 | 17 | 15 | 11 | 10 | 2 |
| 4 | 4 | 3 | 7 | 20 | 10 | 21 | 9 | 6 | 15 | 17 | 22 | 1 | 8 | 23 | 5 | 13 | 0 | 2 | 19 | 14 | 24 | 18 | 16 | 12 | 11 |
| 5 | 5 | 12 | 4 | 8 | 21 | 11 | 22 | 10 | 7 | 16 | 18 | 23 | 2 | 9 | 24 | 6 | 14 | 0 | 3 | 20 | 15 | 1 | 19 | 17 | 13 |
| 6 | 6 | 14 | 13 | 5 | 9 | 22 | 12 | 23 | 11 | 8 | 17 | 19 | 24 | 3 | 10 | 1 | 7 | 15 | 0 | 4 | 21 | 16 | 2 | 20 | 18 |
| 7 | 7 | 19 | 15 | 14 | 6 | 10 | 23 | 13 | 24 | 12 | 9 | 18 | 20 | 1 | 4 | 11 | 2 | 8 | 16 | 0 | 5 | 22 | 17 | 3 | 21 |
| 8 | 8 | 22 | 20 | 16 | 15 | 7 | 11 | 24 | 14 | 1 | 13 | 10 | 19 | 21 | 2 | 5 | 12 | 3 | 9 | 17 | 0 | 6 | 23 | 18 | 4 |
| 9 | 9 | 5 | 23 | 21 | 17 | 16 | 8 | 12 | 1 | 15 | 2 | 14 | 11 | 20 | 22 | 3 | 6 | 13 | 4 | 10 | 18 | 0 | 7 | 24 | 19 |
| 10 | 10 | 20 | 6 | 24 | 22 | 18 | 17 | 9 | 13 | 2 | 16 | 3 | 15 | 12 | 21 | 23 | 4 | 7 | 14 | 5 | 11 | 19 | 0 | 8 | 1 |
| 11 | 11 | 2 | 21 | 7 | 1 | 23 | 19 | 18 | 10 | 14 | 3 | 17 | 4 | 16 | 13 | 22 | 24 | 5 | 8 | 15 | 6 | 12 | 20 | 0 | 9 |
| 12 | 12 | 10 | 3 | 22 | 8 | 2 | 24 | 20 | 19 | 11 | 15 | 4 | 18 | 5 | 17 | 14 | 23 | 1 | 6 | 9 | 16 | 7 | 13 | 21 | 0 |
| 13 | 13 | 0 | 11 | 4 | 23 | 9 | 3 | 1 | 21 | 20 | 12 | 16 | 5 | 19 | 6 | 18 | 15 | 24 | 2 | 7 | 10 | 17 | 8 | 14 | 22 |
| 14 | 14 | 23 | 0 | 12 | 5 | 24 | 10 | 4 | 2 | 22 | 21 | 13 | 17 | 6 | 20 | 7 | 19 | 16 | 1 | 3 | 8 | 11 | 18 | 9 | 15 |
| 15 | 15 | 16 | 24 | 0 | 13 | 6 | 1 | 11 | 5 | 3 | 23 | 22 | 14 | 18 | 7 | 21 | 8 | 20 | 17 | 2 | 4 | 9 | 12 | 19 | 10 |
| 16 | 16 | 11 | 17 | 1 | 0 | 14 | 7 | 2 | 12 | 6 | 4 | 24 | 23 | 15 | 19 | 8 | 22 | 9 | 21 | 18 | 3 | 5 | 10 | 13 | 20 |
| 17 | 17 | 21 | 12 | 18 | 2 | 0 | 15 | 8 | 3 | 13 | 7 | 5 | 1 | 24 | 16 | 20 | 9 | 23 | 10 | 22 | 19 | 4 | 6 | 11 | 14 |
| 18 | 18 | 15 | 22 | 13 | 19 | 3 | 0 | 16 | 9 | 4 | 14 | 8 | 6 | 2 | 1 | 17 | 21 | 10 | 24 | 11 | 23 | 20 | 5 | 7 | 12 |
| 19 | 19 | 13 | 16 | 23 | 14 | 20 | 4 | 0 | 17 | 10 | 5 | 15 | 9 | 7 | 3 | 2 | 18 | 22 | 11 | 1 | 12 | 24 | 21 | 6 | 8 |
| 20 | 20 | 9 | 14 | 17 | 24 | 15 | 21 | 5 | 0 | 18 | 11 | 6 | 16 | 10 | 8 | 4 | 3 | 19 | 23 | 12 | 2 | 13 | 1 | 22 | 7 |
| 21 | 21 | 8 | 10 | 15 | 18 | 1 | 16 | 22 | 6 | 0 | 19 | 12 | 7 | 17 | 11 | 9 | 5 | 4 | 20 | 24 | 13 | 3 | 14 | 2 | 23 |
| 22 | 22 | 24 | 9 | 11 | 16 | 19 | 2 | 17 | 23 | 7 | 0 | 20 | 13 | 8 | 18 | 12 | 10 | 6 | 5 | 21 | 1 | 14 | 4 | 15 | 3 |
| 23 | 23 | 4 | 1 | 10 | 12 | 17 | 20 | 3 | 18 | 24 | 8 | 0 | 21 | 14 | 9 | 19 | 13 | 11 | 7 | 6 | 22 | 2 | 15 | 5 | 16 |
| 24 | 24 | 17 | 5 | 2 | 11 | 13 | 18 | 21 | 4 | 19 | 1 | 9 | 0 | 22 | 15 | 10 | 20 | 14 | 12 | 8 | 7 | 23 | 3 | 16 | 6 |

| × | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| 2 | 0 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 |
| 3 | 0 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 |
| 4 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 |
| 5 | 0 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 |
| 6 | 0 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 |
| 7 | 0 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 |
| 8 | 0 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 9 | 0 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 10 | 0 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 11 | 0 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 12 | 0 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 13 | 0 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 14 | 0 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| 15 | 0 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 16 | 0 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 17 | 0 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 18 | 0 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 19 | 0 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 20 | 0 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 21 | 0 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 22 | 0 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 23 | 0 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
| 24 | 0 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |

Ayrıca bakınız
--------------

* Soyut cebir
* Sonlu halka
* Sonlu grup

|  |  |
| --- | --- |
| Otorite kontrolü Bunu Vikiveri'de düzenleyin | 
* BNF: cb120618782 (data)
* LCCN: sh85048351
* NLI: 987007531228605171

 |