2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65835If $F$ is a finitely generated free group and $ϕ$ is a positive automorphism of $F$ then $F\rtimes_ϕZ$ satisfies a quadratic isoperimetric inequality.69 pages, 32 figures. Improved proof of the Pincer LemmaGroup Theory20F65; 20F06, 20F28, 57M07text