Dependence over subgroups of free groups
Copyright policy )Dependence over subgroups of free groups
Given a finitely generated subgroup H of a free group F, we present an algorithm which computes [Formula: see text], such that the set of elements [Formula: see text], for which there exists a non-trivial H-equation having g as a solution is precisely the disjoint union of the double cosets [Formula: see text]. Moreover, we present an algorithm which, given a finitely generated subgroup [Formula: see text] and an element [Formula: see text], computes a finite set of elements from [Formula: see text] (of the minimum possible cardinality) generating, as a normal subgroup, the “ideal” [Formula: see text] of all “polynomials” [Formula: see text], such that [Formula: see text]. The algorithms, as well as the proofs, are based on the graph-theoretic techniques introduced by Stallings and on the more classical combinatorial techniques of Nielsen transformations. The key notion here is that of dependence of an element [Formula: see text] on a subgroup H. We also study the corresponding notions of dependence sequence and dependence closure of a subgroup.
Generators, relations, and presentations of groups, Free nonabelian groups, Group Theory (math.GR), algebraic extension in free groups, equations over free groups, Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups, Algebraic geometry over groups; equations over groups, dependence in free groups, Nielsen transformations, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra, Algebraic extension in free groups, Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups, FOS: Mathematics, Dependence in free groups, Stallings foldings, Equations over free groups, Geometric group theory, Mathematics - Group Theory, 20F70
Generators, relations, and presentations of groups, Free nonabelian groups, Group Theory (math.GR), algebraic extension in free groups, equations over free groups, Classificació AMS::20 Group theory and generalizations::20F Special aspects of infinite or finite groups, Algebraic geometry over groups; equations over groups, dependence in free groups, Nielsen transformations, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra, Algebraic extension in free groups, Classificació AMS::20 Group theory and generalizations::20E Structure and classification of infinite or finite groups, FOS: Mathematics, Dependence in free groups, Stallings foldings, Equations over free groups, Geometric group theory, Mathematics - Group Theory, 20F70
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!