Goodman-Kahn theorem

The Goodman-Kahn theorem states that in certain mathematical settings involving infinite structures (like infinite groups), the way a subgroup fits inside a larger group is uniquely determined by some abstract properties. Specifically, it reveals that under specific conditions, the subgroup's position and structure are rigidly fixed, preventing alternative arrangements. This result helps mathematicians understand the inherent symmetries and relationships within infinite systems, providing insights into their fundamental composition and how they can be classified or distinguished from one another.