3-subnormal not implies finite-automorph-join-closed subnormal
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., 3-subnormal subgroup) need not satisfy the second subgroup property (i.e., finite-automorph-join-closed subnormal subgroup)
View a complete list of subgroup property non-implications | View a complete list of subgroup property implications
Get more facts about 3-subnormal subgroup|Get more facts about finite-automorph-join-closed subnormal subgroup
EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property 3-subnormal subgroup but not finite-automorph-join-closed subnormal subgroup|View examples of subgroups satisfying property 3-subnormal subgroup and finite-automorph-join-closed subnormal subgroup
A join of finitely many 3-subnormal subgroups that are all automorphs of each other need not be a Subnormal subgroup (?). In fact, even a join of two 3-subnormal subgroups that are automorphs of each other need not be a subnormal subgroup.
- Join of two 3-subnormal subgroups may be proper and contranormal
- 4-subnormal not implies finite-conjugate-join-closed subnormal
- 2-subnormality is conjugate-join-closed
- 2-subnormal implies join-transitively subnormal
- 3-subnormal implies finite-conjugate-join-closed subnormal
The counterexample for this is the same as the counterexample in join of two 3-subnormal subgroups may be proper and contranormal.