Subnormal Subgroups of Finite Rank

1. Subnormal Subgroups of Finite Rank Youngmi Kim Jacksonville State University

2. DEFINITION

3. DEFINITION

4. Locally nilpotent groups Baer groups (every cyclic subgroup is subnormal) Groups in which every subgroup is subnormal Nilpotent groups

5. Roseblade’s Theorem

6. Roseblade’s Theorem (1965) If G is a group in which every subgroup is subnormal of bounded defect, then G is nilpotent of bounded class.

7. DEFINITION

9. DEFINITION

10. Main Theorem

11. Main Theorem (Less formally) An X-group of infinite rank has bounded class if its subgroups of infinite rank are subnormal of bounded defect.

12. Corollary