@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",

}