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→The case n \ne 1,2, 4

* [[Commutator subgroup centralizes cyclic normal subgroup]]: In particular, the cyclic part in a dihedral group is contained in the [[centralizer of commutator subgroup]] for all <math>n</math>. The cases <math>n = 2,4</math> need to be excluded because these are the only cases where the centralizer of commutator subgroup is ''bigger'', i.e., the whole group.

* [[Abelian subgroup equals centralizer of commutator subgroup in generalized dihedral group unless it is a 2-group of exponent at most four]]

* [[Abelian subgroup is contained in centralizer of commutator subgroup in generalized dihedral group]]

===Odd versus even <math>n</math>===

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