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Register a new userThe prolongation of central extensions
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The aim of this paper is to study the $(alpha, gamma)$-prolongation of central extensions. We obtain the obstruction theory for $(alpha, gamma)$-prolongations and classify $(alpha, gamma)$-prolongations thanks to low-dimensional cohomology groups of groups.
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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. Thompsons 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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