Timeline for A question on automorphisms of finite abelian groups
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 19, 2013 at 4:50 | vote | accept | Marius Tarnauceanu | ||
| Mar 18, 2013 at 16:17 | comment | added | Tom Goodwillie | (when $k\ge 2$) | |
| Mar 18, 2013 at 14:07 | comment | added | Tom Goodwillie | Yes. It's enough if $G^k$ has the property when $G$ is cyclic. $G^k$ always has the property if $G$ is abelian, because there exists an invertible $k\times k$ matrix $M$ over $\mathbb Z$ such that $1-M$ is invertible. | |
| Mar 18, 2013 at 6:49 | history | edited | Marius Tarnauceanu | CC BY-SA 3.0 |
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| Mar 18, 2013 at 6:39 | history | edited | Marius Tarnauceanu | CC BY-SA 3.0 |
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| Mar 18, 2013 at 6:21 | comment | added | Marius Tarnauceanu | Thank you very much. This is the strong form of a problem from a mathematics contest. I think that Tom is right: in a finite abelian 2-group $G$ satisfying the above property each $\alpha_i$ occurs at least twice. My problem is whether the converse is true (i.e. if a finite abelian 2-group $G$ such that each $\alpha_i$ occurs at least twice satisfies this property). | |
| Mar 16, 2013 at 15:44 | comment | added | Tom Goodwillie | It's not true. You need to strengthen $(\ast)$ to say that each positive integer that occurs as an $\alpha_j$ occurs at least twice. | |
| Mar 16, 2013 at 13:58 | comment | added | Amritanshu Prasad | Curious why you need this. | |
| Mar 16, 2013 at 13:40 | comment | added | Jeremy Rickard | I'm not clear about what you can't prove? Is it whether $(*)$ is a sufficient condition for abelian 2-groups? In any case, for finite abelian groups I think the question reduces easily to the Sylow $p$-subgroups. | |
| Mar 16, 2013 at 11:20 | answer | added | Amritanshu Prasad | timeline score: 3 | |
| Mar 16, 2013 at 7:58 | history | asked | Marius Tarnauceanu | CC BY-SA 3.0 |