Is there some bound on the growth of finitely generated group extensions? For instance Heisenberg integer group has polynomial growth of degree 4 and fits into the exact sequence $Z \rightarrow H \rightarrow Z \times Z $. Can we say that each extension $ Z \rightarrow Q \rightarrow Z^{n} $ has polynomial growth of degree at most $n+1$ or anything in this spirit concerning group extensions?
2026-03-27 08:42:54.1774600974
Asymptotic growth of group extensions
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