Corpus ID: 235755298

Dependence and algebraicity over subgroups of free groups

  title={Dependence and algebraicity over subgroups of free groups},
  author={A. Rosenmann and Enric Ventura Capell},
An element g of a free group F depends on a subgroup H < F , or is algebraic over H , if it satisfies a univariate equation over H . Equivalently, when H is finitely-generated, the rank of 〈H, g〉 is at most the rank of H . We study the elements that depend on subgroups of F , the subgroups they generate and the equations that they satisfy. 


On the intersection of subgroups in free groups: Echelon subgroups are inert
  • A. Rosenmann
  • Chemistry, Computer Science
  • Groups Complex. Cryptol.
  • 2013
The known families of inert subgroups are expanded and it is shown that the inertia property holds for 1-generator endomorphisms and echelon subgroups in free groups are inert. Expand
On Rank, Root and Equations in Free Groups
  • A. Rosenmann
  • Mathematics, Computer Science
  • Int. J. Algebra Comput.
  • 2001
It is shown that if in "Lyndon equation" the exponents ai satisfy gcd(a1,…,an)≠1 then the inner rank is ⌊ n/2⌋. Expand
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