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Thread: free abelian group as semi-direct products?

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    free abelian group as semi-direct products?

    I have a HNN extension $\displaystyle G=<t,A;t^{-1}ht=h>$ where $\displaystyle A=L<h>$ is a semi-direct product of $\displaystyle L$ by $\displaystyle <h>$ and $\displaystyle <h>$ is cyclic.

    $\displaystyle G$ can be written as free products of $\displaystyle A$ and $\displaystyle B$ amalgamating $\displaystyle <h>$ where $\displaystyle B=<t,h;t^{-1}ht=h>$ is a free abelian group.

    Can $\displaystyle B$ expressed as a semi-direct product of cyclic free group $\displaystyle <t;->$ by $\displaystyle <h>$?
    Last edited by deniselim17; Jul 25th 2009 at 10:47 PM.
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