Timeline for Stallings' Theorem for free products of groups
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 11, 2014 at 10:10 | comment | added | user75691 | That's perfect. Thank you again for your time and for your help. | |
| Jul 10, 2014 at 20:59 | comment | added | HJRW | Yes, the 'finite-sheeted' condition means algebraically that the restriction to each vertex group is finite-index. | |
| Jul 10, 2014 at 15:15 | comment | added | user75691 | Yes, I understand. We just need to put some conditions in vertex groups/spaces. I have a final question if this is possible, this condition for example corresponds algebraically to finite index, I mean something like this is enough? I would like to thank both of you, for your answers, they are very helpful for me. | |
| Jul 10, 2014 at 13:10 | comment | added | HJRW | Yes, as @BenjaminSteinberg says, finite Kurosh rank is enough, but you need the 'finite-sheeted' hypothesis. | |
| Jul 10, 2014 at 11:45 | comment | added | Benjamin Steinberg | But you would need to interpret finite sheeted relative to vertex groups. | |
| Jul 10, 2014 at 11:39 | comment | added | Benjamin Steinberg | Finite Kurosh rank should be enough. It is sufficient for the argument in my paper. You basically need a finite core of some sort. | |
| Jul 10, 2014 at 10:31 | comment | added | user75691 | I am asking this question because in the case of graph of groups it is enough to suppose finite Kurosh rank which implies finite graph of groups. | |
| Jul 10, 2014 at 9:57 | comment | added | user75691 | Thanks a lot both of for your answers. This theorem is very similar to that I want. Can I ask you something? I would like to ask if we need the hypothesis of finitely generated, because we want that every vertex space to be finite? | |
| Jul 10, 2014 at 9:56 | vote | accept | user75691 | ||
| Jul 9, 2014 at 21:09 | comment | added | HJRW | @BenjaminSteinberg, well, I've added a rough definition. I can't define it formally without recalling the definition of graphs of spaces etc. | |
| Jul 9, 2014 at 21:08 | history | edited | HJRW | CC BY-SA 3.0 |
Added rough definition of a precovering.
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| Jul 9, 2014 at 20:58 | comment | added | Benjamin Steinberg | @HRJW, perhaps you should define a precovering? | |
| Jul 9, 2014 at 20:46 | comment | added | HJRW | @BenjaminSteinberg - no, it's all bound up in the definition of a precovering! | |
| Jul 9, 2014 at 19:53 | comment | added | Benjamin Steinberg | @HRJW, you need some separability hypotheses here don't you? | |
| Jul 9, 2014 at 19:48 | history | answered | HJRW | CC BY-SA 3.0 |