Solvable Groups of Exponential Growth and Hnn Extensions

@inproceedings{Alperin1998SolvableGO,
  title={Solvable Groups of Exponential Growth and Hnn Extensions},
  author={Roger C. Alperin},
  year={1998}
}
An extraordinary theorem of Gromov, [4], characterizes the finitely generated groups of polynomial growth; a group has polynomial growth iff it is nilpotent by finite. This theorem went a long way from its roots in the class of discrete subgroups of solvable Lie groups. Wolf, [11], proved that a polycyclic group of polynomial growth is nilpotent by finite. This theorem is primarily about linear groups and another proof by Tits appears as an appendix to Gromov’s paper. In fact if G is torsion… CONTINUE READING

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