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On the intersection of subgroups in free groups: Echelon subgroups are inert
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Amnon Rosenmann
Published/Copyright:
October 11, 2013
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.
Keywords: Free groups; subgroups intersection; echelon subgroups; inert subgroups; compressed subgroups; 1-generator endomorphisms; fixed subgroups of automorphisms
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
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Keywords for this article
Free groups;
subgroups intersection;
echelon subgroups;
inert subgroups;
compressed subgroups;
1-generator endomorphisms;
fixed subgroups of automorphisms
Articles in the same Issue
- Masthead
- Another look at non-uniformity
- An asymmetric generalisation of Artin monoids
- Non-associative key establishment for left distributive systems
- On the dimension of matrix representations of finitely generated torsion free nilpotent groups
- On the intersection of subgroups in free groups: Echelon subgroups are inert
- A secret sharing scheme based on the Closest Vector Theorem and a modification to a private key cryptosystem
