Hall does not satisfy transfer condition
This article gives the statement, and possibly proof, of a subgroup property (i.e., Hall subgroup) not satisfying a subgroup metaproperty (i.e., transfer condition).
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It is possible to have a finite group , a Hall subgroup , and a subgroup of such that is not a Sylow subgroup of .
- Hall satisfies transitivity
- Transitive and transfer condition implies intersection-closed
- Hall is not intersection-closed
The proof follows directly by combining facts (1), (2), and (3).