Corpus ID: 119151462

Preservation of Trees by semidirect Products

  title={Preservation of Trees by semidirect Products},
  author={Gabriel Zapata},
  journal={arXiv: Group Theory},
  • Gabriel Zapata
  • Published 29 December 2017
  • Mathematics
  • arXiv: Group Theory
We show that the semidirect product of a group $C$ by $A*_D B$ is isomorphic to the free product of $A\rtimes C$ and $B\rtimes C$ amalgamated at $D\rtimes C$, where $A$, $B$ and $C$ are arbitrary groups. Moreover, we apply this theorem to prove that any group $G$ that acts without inversion on a tree $T$ that possesses a segment $\Gamma$ for its quotient graph, such that, if the stabilizers of the vertex set $\{\,P,Q\,\}$ and edge $y$ of a lift of $\, \Gamma$ in $T$ are of the form $G_{P… Expand


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  • 1995