# Preservation of Trees by semidirect Products

@article{Zapata2017PreservationOT, title={Preservation of Trees by semidirect Products}, author={Gabriel Zapata}, journal={arXiv: Group Theory}, year={2017} }

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

#### References

SHOWING 1-4 OF 4 REFERENCES

An Introduction to the Theory of Groups

- Mathematics
- 1965

Anyone who has studied "abstract algebra" and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of the… Expand

Categories for the Working Mathematician

- Mathematics
- 1971

I. Categories, Functors and Natural Transformations.- 1. Axioms for Categories.- 2. Categories.- 3. Functors.- 4. Natural Transformations.- 5. Monics, Epis, and Zeros.- 6. Foundations.- 7. Large… Expand

Combinatorial Group Theory

- Mathematics
- 1977

Chapter I. Free Groups and Their Subgroups 1. Introduction 2. Nielsen's Method 3. Subgroups of Free Groups 4. Automorphisms of Free Groups 5. Stabilizers in Aut(F) 6. Equations over Groups 7.… Expand

Combinatorial Group Theory , Ergebnisse der Mathematik , band 89 , Springer 1977

- Combinatorial Group Theory
- 1995