Mathematics – Group Theory
Scientific paper
2012-02-15
Mathematics
Group Theory
Scientific paper
Let Gamma be a connected, locally finite graph of finite tree width and G be a group acting on it with finitely many orbits and finite node stabilizers. We provide an elementary and direct construction of a tree T on which G acts with finitely many orbits and finite vertex stabilizers. Moreover, the tree is defined directly in terms of the structure tree of optimally nested cuts of Gamma. Once the tree is constructed, standard Bass-Serre theory yields that G is virtually free. This approach simplifies the existing proofs for the fundamental result of Muller and Schupp that characterizes context-free groups as f.g. virtually free groups. Our construction avoids the explicit use of Stallings' structure theorem and it is self-contained. We also give a simplified proof for an important consequence of the structure tree theory by Dicks and Dunwoody which has been stated by Thomassen and Woess. It says that a f.g. group is accessible if and only if its Cayley graph is accessible.
Diekert Volker
Weiß Armin
No associations
LandOfFree
Context-Free Groups and Their Structure Trees does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Context-Free Groups and Their Structure Trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Context-Free Groups and Their Structure Trees will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-557236