Sous-groupe <h2, d2>
Quelques calculs dans H2D2 Table de Cayley de H2D2 Sous-groupes de H2D2 Classes de conjugaison de H2D2 Centre de H2D2 Structure de H2D2 et isomorphismes |
1 | x | x2 | x3 | x4 | x5 | h2 | x5 h2 | x4 h2 | x3 h2 | x2 h2 | x h2 | |
1 | 1 | x | x2 | x3 | x4 | x5 | h2 | x5 h2 | x4 h2 | x3 h2 | x2 h2 | x h2 |
x | x | x2 | x3 | x4 | x5 | 1 | x h2 | h2 | x5 h2 | x4 h2 | x3 h2 | x2 h2 |
x2 | x2 | x3 | x4 | x5 | 1 | x | x2 h2 | x h2 | h2 | x5 h2 | x4 h2 | x3 h2 |
x3 | x3 | x4 | x5 | 1 | x | x2 | x3 h2 | x2 h2 | x h2 | h2 | x5 h2 | x4 h2 |
x4 | x4 | x5 | 1 | x | x2 | x3 | x4 h2 | x3 h2 | x2 h2 | x h2 | h2 | x5 h2 |
x5 | x5 | 1 | x | x2 | x3 | x4 | x5 h2 | x4 h2 | x3 h2 | x2 h2 | x h2 | h2 |
h2 | h2 | x5 h2 | x4 h2 | x3 h2 | x2 h2 | x h2 | 1 | x | x2 | x3 | x4 | x5 |
x5 h2 | x5 h2 | x4 h2 | x3 h2 | x2 h2 | x h2 | h2 | x5 | 1 | x | x2 | x3 | x4 |
x4 h2 | x4 h2 | x3 h2 | x2 h2 | x h2 | h2 | x5 h2 | x4 | x5 | 1 | x | x2 | x3 |
x3 h2 | x3 h2 | x2 h2 | x h2 | h2 | x5 h2 | x4 h2 | x3 | x4 | x5 | 1 | x | x2 |
x2 h2 | x2 h2 | x h2 | h2 | x5 h2 | x4 h2 | x3 h2 | x2 | x3 | x4 | x5 | 1 | x |
x h2 | x h2 | h2 | x5 h2 | x4 h2 | x3 h2 | x2 h2 | x | x2 | x3 | x4 | x5 | 1 |
Les sous-groupes de H2D2 sont :
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Les classes de conjugaison de H2D2 sont : {1}, {x, x5}, {x2, x4}, {x3}, {h2, x2h2, x4h2}, {xh2, x3h2, x5h2} |
Z (H2D2) = {1, x3} |
H2D2 < x > < h2 > c'est-à-dire : H2D2 Z / 6Z Z / 2Z D6 |
( < x > < h2 > , * ) | --> | ( H2D2 , . ) |
( xk, n) | |--> | xk . n |
H2D2 <h2, x2> x <x3> c'est-à-dire : H2D2 S3 x Z / 2Z |