# Hall not implies WNSCDIN

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., Hall subgroup) neednotsatisfy the second subgroup property (i.e., WNSCDIN-subgroup)

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

Get more facts about Hall subgroup|Get more facts about WNSCDIN-subgroup

EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property Hall subgroup but not WNSCDIN-subgroup|View examples of subgroups satisfying property Hall subgroup and WNSCDIN-subgroup

## Statement

There exists a finite group and a Hall subgroup of such that is *not* a WNSCDIN-subgroup of . In other words, there exist subsets of such that and are conjugate in but not in .

## Related facts

- Sylow implies WNSCDIN: This is a combination of the facts Sylow implies pronormal and pronormal implies WNSCDIN.
- Hall not implies procharacteristic
- Hall not implies pronormal

## Proof

(The same general example used to show that Hall subgroups need not be pronormal works here).**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE]