A Reidemeister-Schreier theorem for finitely $L$-presented groups

Abstract

We prove a variant of the well-known Reidemeister-Schreier theorem for finitely L-presented groups. More precisely, we prove that each finite index subgroup of a finitely L-presented group is itself finitely L-presented. Our proof is constructive and it yields a finite L-presentation for the subgroup.We further study conditions on a finite index subgroup of an invariantly finitely L-presented group to be invariantly L-presented itself.