Normal not implies strongly potentially characteristic
This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., normal subgroup) need not satisfy the second subgroup property (i.e., characteristic-potentially characteristic subgroup)
View a complete list of subgroup property non-implications | View a complete list of subgroup property implications
Get more facts about normal subgroup|Get more facts about characteristic-potentially characteristic subgroup
EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property normal subgroup but not characteristic-potentially characteristic subgroup|View examples of subgroups satisfying property normal subgroup and characteristic-potentially characteristic subgroup
Statement with symbols
The proof follows directly from facts (1) and (2).