Geodesic
Strongly scale-invariant virtually polycyclic groups
Jonas Deré1
1KU Leuven Kulak, Kortrijk, Belgium
Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 985-1004

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DOI

A finitely generated group Γ is called strongly scale-invariant if there exists an injective endomorphism φ:Γ→Γ with the image φ(Γ) of finite index in Γ and the subgroup ⋂n>0​φn(Γ) finite. The only known examples of such groups are virtually nilpotent, or equivalently, all examples have polynomial growth. A question by Nekrashevych and Pete asks whether these groups are the only possibilities for such endomorphisms, motivated by the positive answer due to Gromov in the special case of expanding group morphisms.
DOI : 10.4171/ggd/684
Classification : 20-XX, 00-XX
Mots-clés : polycyclic groups, nilpotent groups, scale-invariant groups, Reidemeister-zeta function, algebraic hull

Jonas Deré  1

1 KU Leuven Kulak, Kortrijk, Belgium 
Jonas Deré. Strongly scale-invariant virtually polycyclic groups. Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 985-1004. doi: 10.4171/ggd/684
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