Center not is 1-automorphism-invariant
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., 1-automorphism-invariant subgroup)
View subgroup property satisfactions for subgroup-defining functions View subgroup property dissatisfactions for subgroup-defining functions
- Quasiautomorphism-invariant not implies 1-automorphism-invariant
- Center is quasiautomorphism-invariant
There exist 1-automorphisms of that do not preserve . In fact, we can achieve any permutation of the cyclic subgroups of order using a 1-automorphism.