Timeline for Distributivity of group topologies on $\Bbb Z$
Current License: CC BY-SA 3.0
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| S Nov 14, 2014 at 3:07 | history | bounty ended | Minimus Heximus | ||
| S Nov 14, 2014 at 3:07 | history | notice removed | Minimus Heximus | ||
| Nov 12, 2014 at 3:18 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Nov 10, 2014 at 19:33 | vote | accept | Minimus Heximus | ||
| Nov 8, 2014 at 21:01 | comment | added | Minimus Heximus | @AndreasThom: I am working on some generalization of group topologies which I call f-subgroups. the lattice of f-subgoups is not distributive on any non-locally-cyclic group. This is a counterexample for locally cyclic case. I can investigate more deeply which groups allow distributive lattices. | |
| Nov 8, 2014 at 20:48 | comment | added | Andreas Thom | Where does the question come from? | |
| Nov 8, 2014 at 18:43 | answer | added | Andreas Thom | timeline score: 15 | |
| Nov 7, 2014 at 1:23 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| S Nov 7, 2014 at 1:04 | history | bounty started | Minimus Heximus | ||
| S Nov 7, 2014 at 1:04 | history | notice added | Minimus Heximus | Reward existing answer | |
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| Oct 5, 2014 at 15:55 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Oct 5, 2014 at 12:33 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Oct 5, 2014 at 12:24 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Oct 5, 2014 at 11:06 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Oct 4, 2014 at 21:05 | history | undeleted | Minimus Heximus | ||
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| S Oct 4, 2014 at 20:38 | history | bounty ended | CommunityBot | ||
| S Oct 4, 2014 at 20:38 | history | notice removed | CommunityBot | ||
| Oct 2, 2014 at 13:36 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Sep 27, 2014 at 13:17 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Sep 26, 2014 at 21:31 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| S Sep 26, 2014 at 18:45 | history | bounty started | Minimus Heximus | ||
| S Sep 26, 2014 at 18:45 | history | notice added | Minimus Heximus | Canonical answer required | |
| Sep 26, 2014 at 16:23 | comment | added | Sebastien Palcoux | "something in the structure of $\mathbb{Z}$ other than abelianness, must be used to prove distributivity": Yes, perhaps the distributivity of its subgroups lattice. More generally (Ore's theorem) a group is locally cyclic iff its subgroups lattice is distributive (see a proof here) | |
| Sep 26, 2014 at 10:32 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Sep 26, 2014 at 10:24 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Sep 25, 2014 at 15:37 | comment | added | Sebastien Palcoux | There is also this result of Lukacs-Palfy: a group $G$ is abelian iff the subgroups lattice of $G \times G$ is modular (see a proof here). | |
| Sep 17, 2014 at 7:41 | comment | added | Dominic van der Zypen | Note that $(\mathcal{L}, \subseteq)$ is distributive if and only if the lattice $M_3$ ( en.wikipedia.org/wiki/Distributive_lattice#mediaviewer/… ) cannot be embedded in $(\mathcal{L}, \subseteq)$. So one idea might be to find three group topologies $\tau_1,\tau_2,\tau_3$ with identical infimum and identical supremum, or show that this cannot be done. | |
| Sep 12, 2014 at 15:45 | comment | added | Minimus Heximus | A group topology on a group $G$ is a topology $\mathcal T$ on the set $G$ with which $(G,\mathcal T)$ is a topological group, that is, the function $(x,y)\mapsto xy^{-1}$ is continuous. | |
| Sep 12, 2014 at 15:42 | comment | added | The Masked Avenger | What is a group topology on Z? Can it be isomorphic to a group topology on Q? On Z_p? | |
| Sep 12, 2014 at 9:51 | history | edited | Minimus Heximus | CC BY-SA 3.0 |
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| Sep 12, 2014 at 7:59 | history | edited | Minimus Heximus |
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| Sep 11, 2014 at 21:02 | history | edited | Minimus Heximus |
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| Sep 11, 2014 at 16:18 | history | asked | Minimus Heximus | CC BY-SA 3.0 |
