Geodesic
Strong boundedness and algebraically closed groups
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 205-209.

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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.
Classification : 20A15, 20E08, 20F65
Keywords: strongly bounded groups; existentially closed groups 
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     author = {Majcher-Iwanow, Barbara},
     title = {Strong boundedness and algebraically closed groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {205--209},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
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     mrnumber = {2338088},
     zbl = {1174.20011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2007__48_2_a1/}
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Majcher-Iwanow, Barbara. Strong boundedness and algebraically closed groups. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 205-209. http://geodesic.mathdoc.fr/item/CMUC_2007__48_2_a1/