# Hall does not satisfy transfer condition

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., Hall subgroup)notsatisfying a subgroup metaproperty (i.e., transfer condition).

View all subgroup metaproperty dissatisfactions | View all subgroup metaproperty satisfactions|Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about Hall subgroup|Get more facts about transfer condition|

## Contents

## Statement

It is possible to have a finite group , a Hall subgroup , and a subgroup of such that is not a Sylow subgroup of .

## Related facts

## Facts used

- Hall satisfies transitivity
- Transitive and transfer condition implies intersection-closed
- Hall is not intersection-closed

## Proof

### Hands-on proof

### Property-theoretic proof

The proof follows directly by combining facts (1), (2), and (3).