Abstract:A finitely generated group is called strongly scale-invariant if there exists an injective endomorphism ' W ! with the image './ of finite index in and the subgroup T n>0 ' n ./ 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.In… Show more
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