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On the Intersection of Finitely Generated Free GroupsJournal of The London Mathematical Society-second Series
- Publisher
- de Gruyter
- Copyright
- Copyright © 2013 by the
- ISSN
- 1867-1144
- eISSN
- 1869-6104
- DOI
- 10.1515/gcc-2013-0013
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. 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.
Journal
Groups Complexity Cryptology – de Gruyter
Published: Nov 1, 2013