Groups with property (T) and many alternating group quotients

Puntos clave

• A large subgroup of tame automorphisms demonstrates Kazhdan's property (T), enhancing our understanding of group structures.
• The study establishes the existence of a group with property (T) that can map onto large powers of alternating groups.
• This work builds on the concept of operads, expanding the theory around free algebras and their automorphic behaviors.
• Implications suggest deeper connections exist in group theory, especially relating property (T) to alternating group quotients.