Group Extensions and Graphs

Group Extensions and Graphs

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Group Extensions and Graphs

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Ballester-Bolinches, Adolfo Perfil; Cosme i Llópez, Enric; Esteban Romero, Ramón Perfil
This document is a artículoDate2016

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A classical result of Gaschütz affirms that given a finite A-generated group G and a prime p, there exists a group G# and an epimorphism φ:G#⟶G whose kernel is an elementary abelian p-group which is universal among all groups satisfying this property. This Gaschütz universal extension has also been described in the mathematical literature with the help of the Cayley graph. We give an elementary and self-contained proof of the fact that this description corresponds to the Gaschütz universal extension. Our proof depends on another elementary proof of the Nielsen-Schreier theorem, which states that a subgroup of a free group is free.

    Ballester-Bolinches, Adolfo Cosme i Llópez, Enric Esteban Romero, Ramón 2016 Group Extensions and Graphs Expositiones Mathematicae 34 3 327 334

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