# Article

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Keywords:
strongly bounded groups; existentially closed groups
Summary:
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.
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