Dependence and algebraicity over subgroups of free groups

Amnon Rosenmann, Enric Ventura Capell

Research output: Working paperPreprint


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 $\gen{H,g}$ 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.
Original languageEnglish
Publication statusPublished - 7 Jul 2021

Publication series e-Print archive
PublisherCornell University Library


  • math.GR
  • 20F70


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