The Geometric Invariants of Group Extensions Part I: Finite Extensions

Details The Geometric Invariants of Group Extensions Part I: Finite Extensions The Geometric Invariants of Group Extensions Part I: Finite Extensions

2011-03-01

arxiv.org/abs/1103.0313v3

Mathematics

Group Theory

This paper has been withdrawn by the authors to further work on the main theorems

Scientific paper

In this note, we compute the {\Sigma}^1(G) invariant when 1 {\to} H {\to} G {\to} K {\to} 1 is a short exact sequence of finitely generated groups with K finite. As an application, we construct a group F semidirect Z_2 where F is the R. Thompson's group F and show that F semidirect Z_2 has the R-infinity property while F is not characteristic. Furthermore, we construct a finite extension G with finitely generated commutator subgroup G' but has a finite index normal subgroup H with infinitely generated H'.

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