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Dihedral group - Groupprops

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This is a family of groups parametrized by the natural numbers, viz, for each natural number, there is a unique group (upto isomorphism) in the family corresponding to the natural number. The natural number is termed the parameter for the group family The dihedral group of degree and order , denoted sometimes as (this wiki uses ), sometimes as , and sometimes as , is defined in the following equivalent ways: The dihedral groups arise as a special case of a family of groups called von Dyck groups. They also arise as a special case of a family of groups called Coxeter groups. Note that for and , the geometric description of the dihedral group does not make sense. In these cases, we use the algebraic description. The infinite dihedral group, which is the case of the dihedral group and is denoted and is defined as: . Note that all dihedral groups are metacyclic and hence supersolvable. A dihedral group is nilpotent if and only if it is of order for some . It is abelian only if it has

Dihedral group - Groupprops Jump to content Want site search autocompletion? See here Encountering 429 Too Many Requests errors when browsing the site? See here From Groupprops WARNING: POTENTIAL TERMINOLOGICAL CONFUSION : Please don't confuse this with dicyclic group (also called binary dihedral group) This article defines a group property : a property that can be evaluated to true/false for any given group , invariant under isomorphism View a complete list of group properties VIEW RELATED : Group property implications | Group property non-implications | Group metaproperty satisfactions | Gro

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