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

On the intersection of subgroups in free groups: Echelon subgroups are inert 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

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

Groups Complexity Cryptology , Volume 5 (2) – Nov 1, 2013

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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 Cryptologyde Gruyter

Published: Nov 1, 2013

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