The Geometric Invariants of Group Extensions Part I: Finite Extensions
Group Theory
2011-12-22 v3
Abstract
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'.
Keywords
Cite
@article{arxiv.1103.0313,
title = {The Geometric Invariants of Group Extensions Part I: Finite Extensions},
author = {Nic Koban and Peter Wong},
journal= {arXiv preprint arXiv:1103.0313},
year = {2011}
}
Comments
This paper has been withdrawn by the authors to further work on the main theorems