21 Übersetzungen
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Anwendungsbeispiele Englisch
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- S3 (dihedral group of order 6) is the group of all permutations of 3 objects, but also a permutation group of the 6 group elements, and the latter is how it is realized by its regular representation.
- A regular hexagon has six rotational symmetries ("rotational symmetry of order six") and six reflection symmetries ("six lines of symmetry"), making up the dihedral group D6.
- A simple illustration of Sylow subgroups and the Sylow theorems are the dihedral group of the "n"-gon, "D"2"n".
- It is however an abelian group, and isomorphic to the dihedral group of order (cardinality) 4, i.e.
- For example, the Schur–Zassenhaus theorem implies the existence of a semi-direct product among groups of order 6; there are two such products, one of which is a direct product, and the other a dihedral group.
- Nor need a "p"-group be abelian; the dihedral group Dih4 of order 8 is a non-abelian 2-group. However, every group of order "p"2 is abelian.
- For example, the dihedral group [...] is generated by the right rotation [...] and the reflection [...] in a vertical line (every element of [...] is a finite product of copies of these and their inverses).
- For example, the dihedral group D8 of order sixteen can be generated by a rotation, "r", of order 8; and a flip, "f", of order 2; and certainly any element of D8 is a product of "r" [...] s and "f" [...] s.
© dict.cc English-German dictionary 2024
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