Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter October 11, 2013

On the intersection of subgroups in free groups: Echelon subgroups are inert

  • Amnon Rosenmann EMAIL logo


A subgroup H of a free group F is called inert in F if for every . In this paper we expand the known families of inert subgroups. We show that the inertia property holds for 1-generator endomorphisms. Equivalently, echelon subgroups in free groups are inert. An echelon subgroup is defined through a set of generators that are in echelon form with respect to some ordered basis of the free group, and may be seen as a generalization of a free factor. For example, the fixed subgroups of automorphisms of finitely generated free groups are echelon subgroups. The proofs follow mostly a graph-theoretic or combinatorial approach.

Received: 2013-01-30
Revised: 2013-05-25
Published Online: 2013-10-11
Published in Print: 2013-11-01

© 2013 by Walter de Gruyter Berlin Boston

Downloaded on 24.3.2023 from
Scroll Up Arrow