Let $G_1 \le G_2 \le \cdots $ be countable groups with Kazhdan property (T). Let $G = \bigcup_i G_i$. Does it necessarily follow that $G$ has (T)?
This seems false but I cannot find a counterexample.
Let $G_1 \le G_2 \le \cdots $ be countable groups with Kazhdan property (T). Let $G = \bigcup_i G_i$. Does it necessarily follow that $G$ has (T)?
This seems false but I cannot find a counterexample.