Geodesic
Structure of normally and finitely non-co-Hopfian groups
Wouter van Limbeek1
1University of Illinois at Chicago, USA
Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 465-489

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DOI

A group G is (finitely) co-Hopfian if it does not contain any proper (finite-index) subgroups isomorphic to itself. We study finitely generated groups G that admit a descending chain of proper normal finite-index subgroups, each of which is isomorphic to G. We prove that up to finite index, these are always obtained by pulling back a chain of subgroups from a free abelian quotient. We give two applications: first, we show any proper self-embedding of G with finite-index characteristic image arises by pulling back an endomorphism of the abelianization; secondly, we prove special cases (for normal subgroups) of conjectures of Benjamini and Nekrashevych–Pete regarding the classification of scale-invariant groups.
DOI : 10.4171/ggd/603
Classification : 20-XX, 22-XX
Mots-clés : Finitely non-co-Hopfian group, characteristic self-embedding, scale-invariant group, contraction group

Wouter van Limbeek  1

1 University of Illinois at Chicago, USA 
Wouter van Limbeek. Structure of normally and finitely non-co-Hopfian groups. Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 465-489. doi: 10.4171/ggd/603
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     title = {Structure of normally and finitely {non-co-Hopfian} groups},
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     year = {2021},
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     number = {2},
     doi = {10.4171/ggd/603},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/603/}
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