Freiheitssatz
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In mathematics, the Freiheitssatz (German: "freedom/independence theorem": Freiheit + Satz) is a result in the presentation theory of groups, stating that certain subgroups of a one-relator group are free groups.
Consider a group presentation
given by n generators xi and a single cyclically reduced relator r. If x1 appears in r, then (according to the freiheitssatz) the subgroup of G generated by x2, ..., xn is a free group, freely generated by x2, ..., xn. In other words, the only relations involving x2, ..., xn are the trivial ones.