  In 1930, Wilhelm Magnus introduced the so-called Freiheitssatz: Let $F$ be a
free group with basis $\mathcal{X}$ and let $r$ be a cyclically reduced element
of $F$ which contains a basis element $x \in \mathcal{X}$, then every
non-trivial element of the normal closure of $r$ in $F$ contains the basis
element $x$. Equivalently, the subgroup freely generated by $\mathcal{X}
\backslash \{x\}$ embeds canonically into the quotient group $F / \langle \!
\langle r \rangle \! \rangle_{F}$. In this article, we want to introduce a
Freiheitssatz for amalgamated products $G=A \ast_{U} B$ of free groups $A$ and
$B$, where $U$ is a maximal cyclic subgroup in $A$ and $B$: If an element $r$
of $G$ is neither conjugate to an element of $A$ nor $B$, then the factors $A$,
$B$ embed canonically into $G / \langle \! \langle r \rangle \! \rangle_{G}$.
