Timeline for Are the Baumslag-Solitar groups BS(n,n) and BS(n,-n) automata groups?
Current License: CC BY-SA 3.0
7 events
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| Aug 22, 2015 at 7:54 | comment | added | YCor | For a group there's no "standard Bass-Serre tree". But for Baumslag-Solitar groups there's one: indeed they are defined as HNN extension of an infinite cyclic group, and the corresponding Bass-Serre tree is the one I call "standard", the action is with cyclic edge and vertex stabilizers, and in restriction to $L$ the vertex stabilizers are trivial. | |
| Aug 22, 2015 at 6:02 | comment | added | Edgar Ndie | I never heard of "standard Bass-Serre tree" of a group? What is it? | |
| Aug 22, 2015 at 5:58 | comment | added | Edgar Ndie | yes I'm also asking why (1) holds | |
| Aug 19, 2015 at 21:38 | comment | added | YCor | As pointed out by Derek, your question is ambiguous. My guess was that you understand that (1) being virtually $\mathbf{Z}\times F_k$ implies being automata group and that you were asking (2) why $BS(n,\pm n)$ has this virtual property. If you're asking why (1) holds, somebody else could answer better than me. | |
| Aug 19, 2015 at 15:16 | comment | added | Edgar Ndie | Thank you for your answer. Why does this property make $BS(n,n)$ an automaton group? | |
| Aug 19, 2015 at 12:26 | history | edited | YCor | CC BY-SA 3.0 |
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| Aug 19, 2015 at 10:08 | history | answered | YCor | CC BY-SA 3.0 |