A REIDEMEISTER-SCHREIER THEOREM FOR FINITELY L-PRESENTED GROUPS

Authors : René Hartung

Pages : 125-159

View : 25 | Download : 11

Publication Date : 2012-06-01

Article Type : Research Paper

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.
Keywords : Reidemeister Schreier Theorem, infinite presentations, recursive presentations, self similar groups, Basilica group, Grigorchuk group, finite index subgroups