Characteristic equals fully invariant in odd-order abelian group
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a finite Abelian group. That is, it states that in a Finite Abelian group (?), every subgroup satisfying the first subgroup property (i.e., Characteristic subgroup (?)) must also satisfy the second subgroup property (i.e., Fully characteristic subgroup (?)). In other words, every characteristic subgroup of finite Abelian group is a fully characteristic subgroup of finite Abelian group.
View all subgroup property implications in finite Abelian groups View all subgroup property non-implications in finite Abelian groups View all subgroup property implications View all subgroup property non-implications
Statement
In a finite Abelian group, a subgroup is characteristic if and only if it is fully characteristic.