In this paper, we compute the {Sigma}^n(G) and {Omega}^n(G) invariants when 1 rightarrow H rightarrow G rightarrow K rightarrow 1 is a short exact sequence of finitely generated groups with K finite. We also give sufficient conditions for G to have the R_{infty} property in terms of {Omega}^n(H) and {Omega}^n(K) when either K is finite or the sequence splits. As an application, we construct a group F rtimes? Z_2 where F is the R. Thompsons group F and show that F rtimes Z_2 has the R_{infty} property while F is not characteristic.
Download