Timeline for Do positive-density subgroups intersect nontrivially?
Current License: CC BY-SA 4.0
7 events
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| Sep 14, 2019 at 16:17 | comment | added | Sean Eberhard | @MarkSapir Sorry Mark I did not understand your comment, because as I already mentioned in the question the subgroup $F_2$ of $F_2 \times \mathbf{Z}$ has infinite index and positive density. | |
| Sep 14, 2019 at 5:18 | comment | added | Sean Eberhard | @MarkSapir If the balls satisfy $|S^{n+1}| / |S^n| \to 1$ then they define a Folner sequence, which ensures that each subgroup has density = 1/index. There are also some groups of exponential growth, such as free groups, where every subgroup of infinite index has zero density (see the references here: mathoverflow.net/questions/243686/…), but I don't have a very good understanding why. | |
| Sep 14, 2019 at 0:48 | comment | added | user6976 | Do you know an example of a subgroup of infinite index and positive density in a) a group of exponential growth b) a group of superlinear growth c) any f.g. group? | |
| Sep 13, 2019 at 14:50 | comment | added | Sean Eberhard | True, thanks. I actually had in mind $H_1 \cap H_2$ positive-density -- I've added that variant now too. | |
| Sep 13, 2019 at 14:48 | history | edited | Sean Eberhard | CC BY-SA 4.0 |
added 36 characters in body
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| Sep 13, 2019 at 14:10 | comment | added | YCor | You want to assume $G$ infinite to avoid trivial counterexamples. | |
| Sep 13, 2019 at 13:40 | history | asked | Sean Eberhard | CC BY-SA 4.0 |