Profinite Graphs and Groups

1. Preliminaries
Luis Ribes

Part I. Basic Theory

2. Profinite Graphs
Luis Ribes

3. The Fundamental Group of a Profinite Graph
Luis Ribes

4. Profinite Groups Acting on



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-Trees
Luis Ribes

5. Free Products of Pro-



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Groups
Luis Ribes

6. Graphs of Pro-



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Groups
Luis Ribes

Part II. Applications to Profinite Groups

7. Subgroups of Fundamental Groups of Graphs of Groups
Luis Ribes

8. Minimal Subtrees
Luis Ribes

9. Homology and Graphs of Pro-



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Groups
Luis Ribes

10. The Virtual Cohomological Dimension of Profinite Groups
Luis Ribes

Part III. Applications to Abstract Groups

11. Separability Conditions in Free and Polycyclic Groups
Luis Ribes

12. Algorithms in Abstract Free Groups and Monoids
Luis Ribes

13. Abstract Groups vs Their Profinite Completions
Luis Ribes

14. Conjugacy in Free Products and in Free-by-Finite Groups
Luis Ribes

15. Conjugacy Separability in Amalgamated Products
Luis Ribes

Keywords: Mathematics, Topological Groups, Lie Groups, Graph Theory, Group Theory and Generalizations