Abstract:Let $G$ be a non-trivial algebraically closed group and $X$ be a subset of $G$ generating $G$ in infinitely many steps. We give a construction of a binary tree associated with $(G,X)$. Using this we show that if $G$ is $\omega _1$-existentially closed then it is strongly bounded.
Keywords: strongly bounded groups, existentially closed groups
AMS Subject Classification: 20E08, 20F65, 20A15