Central extensions of word hyperbolic groups satisfy a quadratic isoperimetric inequality (Q1924571)

We calculate isoperimetric inequalities for central and nilpotent extensions of finitely presented groups. As applications of these results we prove that a central extension of a word hyperbolic group by a finitely generated abelian group satisfies simultaneous quadratic isoperimetric and linear isodiametric inequalities and we also calculate a new upper bound for isoperimetric inequalities of finitely generated nilpotent groups.