Timeline for Subgroups of a finite abelian group
Current License: CC BY-SA 2.5
24 events
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| Mar 3, 2020 at 2:42 | comment | added | Richard Stanley | A basic result is that a finite abelian $p$-group $G$ of type $\lambda$ contains a subgroup $H$ of type $\mu$ such that $G/H$ has type $\nu$ if and only if the Littlewood-Richardson coefficient $c^\lambda_{\mu,\nu}$ is nonzero. See I. G. Macdonald, Symmetric Functions and Hall Polynomials, second ed., II(4.3) on page 188. | |
| Jun 25, 2016 at 8:54 | comment | added | yakov | If I understood correctly, you ask: Given a decomposition of $G$ in a direct product of cyclic subgroups $Z_1\times\dots\times Z_n$, then any subgroup of $G$ is of the form $L_1\times\dots\times L_n$, where $L_i\le Z_i$ for all $i$. This holds iff $G$ is cyclic. | |
| Nov 19, 2010 at 12:20 | history | edited | user6976 | CC BY-SA 2.5 |
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| Nov 19, 2010 at 8:41 | answer | added | Neil Strickland | timeline score: 7 | |
| Nov 19, 2010 at 5:06 | history | edited | user6976 | CC BY-SA 2.5 |
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| Nov 19, 2010 at 3:10 | history | edited | user6976 | CC BY-SA 2.5 |
Restored the title. Fixed LaTeX.
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| Nov 18, 2010 at 17:12 | history | edited | Anton Geraschenko | CC BY-SA 2.5 |
essentially reverted to revision 5
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| Nov 18, 2010 at 14:09 | history | rollback | user6976 |
Rollback to Revision 1
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| Nov 18, 2010 at 14:08 | history | rollback | user6976 |
Rollback to Revision 4
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| Nov 18, 2010 at 13:43 | comment | added | Todd Trimble | I have edited the question back, as per Anton's explicit request at meta. | |
| Nov 18, 2010 at 13:41 | history | edited | Todd Trimble | CC BY-SA 2.5 |
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| Nov 18, 2010 at 13:12 | history | edited | user6976 | CC BY-SA 2.5 |
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| Nov 18, 2010 at 13:10 | history | rollback | user6976 |
Rollback to Revision 1
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| Nov 17, 2010 at 3:58 | answer | added | Amritanshu Prasad | timeline score: 9 | |
| Nov 16, 2010 at 23:54 | answer | added | user6976 | timeline score: 4 | |
| Nov 16, 2010 at 21:50 | history | edited | Todd Trimble | CC BY-SA 2.5 |
removed some superfluous words, added the word "finite"
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| Nov 16, 2010 at 21:14 | comment | added | Anton Geraschenko | This question went through a close/reopen cycle. Some of the above comments may disappear if they're no longer relevant (i.e. if they related to whether the question should be closed or not). If you want to read them, you can find them at tea.mathoverflow.net/discussion/773/reopen-this-question/… | |
| Nov 16, 2010 at 21:01 | history | reopened |
user6976 Qiaochu Yuan HJRW Anton Geraschenko |
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| Nov 15, 2010 at 20:53 | comment | added | Derek Holt | I wrote the Magma code for this - it does it roughly by enumerating matrices in Hermite Normal Form whose row span contains the list of invariants of the finite abelian group. | |
| Nov 15, 2010 at 15:06 | history | closed |
Franz Lemmermeyer Pete L. Clark José Figueroa-O'Farrill HJRW Mariano Suárez-Álvarez |
too localized | |
| Nov 15, 2010 at 15:01 | comment | added | José Figueroa-O'Farrill | You may want to look at Goursat's Lemma, which determines the subgroups of a direct product group. Then specialise this to the abelian case. | |
| Nov 15, 2010 at 14:51 | comment | added | Franz Lemmermeyer | If Z/3 * Z/9 * Z/4 * Z/8 is too complicated, why don't you try to understand Z/2 * Z/2? BTW, this is not the right medium for questions like that. | |
| Nov 15, 2010 at 14:50 | comment | added | Martin Brandenburg | You may reduce to a fixed prime number, since every abelian torsion group canonically splits into its primary parts. | |
| Nov 15, 2010 at 14:47 | history | asked | uuu | CC BY-SA 2.5 |