Center not is intermediately characteristic
This article gives the statement, and possibly proof, of the fact that for a group, the subgroup obtained by applying a given subgroup-defining function (i.e., center) does not always satisfy a particular subgroup property (i.e., intermediately characteristic subgroup)
View subgroup property satisfactions for subgroup-defining functions View subgroup property dissatisfactions for subgroup-defining functions
The center of a group need not be characteristic in every intermediate subgroup.
Example of the dihedral group
In the dihedral group of order eight, generated by a rotation and reflection , the center is not intermediately characteristic. In fact, it is not characteristic in the intermediate subgroup .