Kazhdan's property

Kazhdan's property, also known as property (T), is a concept in mathematics that describes a certain rigidity in groups—sets of symmetries or transformations. When a group has this property, it means that any way it can act on a space without fixed points must be close to trivial actions. In simpler terms, the property ensures that the group’s structure is tightly constrained, preventing "almost" symmetries from manifesting unless they are genuine symmetries. This rigidity has important implications in areas like geometry, representation theory, and even computer science, where it helps in understanding the stability and structure of complex systems.