Dihedral group
Dihedral group To meet Wikipedia's quality standards and ... The Red Crystal symbol In mathematics, the dihedral group of order 2n is a certain abstract group for which here the notation Dih ...
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Talk:Dihedral group
Talk:Dihedral group I always thought that D_infinity is the symmetry group of a circle, i.e. the semidirect ... Is there a name for this symmetry group then? The infinite dihedral group is usually defined as having ...
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Dihedral group of order 6
Dihedral group of order 6 The smallest non-Abelian group has 6 elements. It is a dihedral group with notation D 3 or D ...
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Symmetry group
Symmetry group This article is about symmetry groups, abstract algebraic structures. See Symmetry group (disambiguation) for other meanings. A tetrahedron can ... The 12 rotations form the rotation (symmetry) group of the figure. The symmetry group of an object (image, signal, etc., e ... in 1D, 2D or 3D) is the group of all isometries under which it ...
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Dicyclic group
Dicyclic group In group theory, a dicyclic group is a member of a class of ... Dic n (n > 1), a non-abelian group of order 4n, which are formed by an extension of a group (generally a cyclic group) by a ...
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Symmetric group
Symmetric group In mathematics, the symmetric group on a set X, denoted by S X or Sym(X), is the group whose underlying set is the set of ... from X to X, in which the group operation is that of composition of functions ... Using this operation, S X forms a group. The operation is also written as ...
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Group isomorphism
Group isomorphism In abstract algebra, a group isomorphism is a function between two groups ... in a way that respects the given group operations. If there exists an isomorphism between ... are called isomorphic. From the standpoint of group theory, isomorphic groups have the same properties ... Given two groups (G, *) and (H, @), a group isomorphism from (G, *) to (H, @) is ...
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Quasidihedral group
Quasidihedral group In mathematics, the quasidihedral groups (also known ... are groups with similar properties to the dihedral groups. In particular they often arise as ... For example, in Galois theory the Galois group G of the polynomial $x^8\; ...\; rational\; field\; is\; isomorphic\; to\; the\; quasidihedral$group of order 16. In this case generators ... 3\rangle. This is almost the group generated by a rotation r by ...
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Weyl group
Weyl group In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system Φ is the subgroup of the isometry group of the root system generated by reflections ... hexagon centered at the origin. The full group of symmetries of this root system is therefore the dihedral group of order 12. The Weyl ...
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P-group
P-group In mathematics, given a prime number p, a p-group is a periodic group in which each element has a power ... is, for each element g of the group, there exists a natural number n such ... center of a non-trivial finite p-group cannot be the trivial subgroup. More ...
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