# Changes

## Subgroup structure of dihedral groups

, 13:41, 2 September 2009
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 [itex]n[/itex]. The cases [itex]n = 2,4[/itex] 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 [itex]n[/itex]===