@techreport{9668977506664fd6a9fb616ff90e1238,
title = "Dependence and algebraicity over subgroups of free groups",
abstract = " 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. ",
keywords = "math.GR, 20F70",
author = "Amnon Rosenmann and {Ventura Capell}, Enric",
note = "11 pages",
year = "2021",
month = jul,
day = "7",
language = "English",
series = "arXiv.org e-Print archive",
publisher = "Cornell University Library",
type = "WorkingPaper",
institution = "Cornell University Library",
}