Solvable Groups of Exponential Growth and HNN Extensions

Mathematics – Group Theory

Scientific paper

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to appear in Groups Korea-98, De Gruyter

Scientific paper

We prove the following version of Milnor's theorem on solvable groups of
exponential growth: A finitely generated solvable group which is not polycyclic
contains an ascending HNN extension. Consequently, a finitely generated
solvable group is ERF iff it is polycyclic.

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