Transitive and transfer condition implies finite-intersection-closed
Transitive subgroup property
Further information: Transitive subgroup property
A subgroup property is termed transitive if whenever are groups such that satisfies property in and satisfies property in , also satisfies property in .
Further information: Transfer condition
Finite-intersection-closed subgroup property
Further information: Finite-intersection-closed subgroup property
A subgroup property is termed finite-intersection-closed if whenever are subgroups satisfying property in , then also satisfies property in .
- Transitive and transfer condition implies finite-relative-intersection-closed
- Finite-relative-intersection-closed implies finite-intersection-closed
Proof using given facts
The proof follows directly by piecing together facts (1) and (2).