# Characteristic not implies elementarily characteristic

From Groupprops

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., characteristic subgroup) neednotsatisfy the second subgroup property (i.e., elementarily characteristic subgroup)

View a complete list of subgroup property non-implications | View a complete list of subgroup property implications

Get more facts about characteristic subgroup|Get more facts about elementarily characteristic subgroup

EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property characteristic subgroup but not elementarily characteristic subgroup|View examples of subgroups satisfying property characteristic subgroup and elementarily characteristic subgroup

## Statement

It is possible to have a characteristic subgroup of a group that is not an elementarily characteristic subgroup of .

## Proof

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