Timeline for Existence of a faithful irreducible representation using Möbius function
Current License: CC BY-SA 3.0
15 events
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| Jun 29, 2017 at 18:22 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
Minor edit: replacement of the broken link.
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Mar 30, 2017 at 10:44 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
The link and notation for the modular maximal-cyclic group was not correct.
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| Mar 28, 2017 at 15:18 | comment | added | Frieder Ladisch | I think the point is that Palfy's formula depends only on the minimal normal subgroups of $G$ (together with the action of $G$ on the abelian ones), while the "easy" formula depends on all normal subgroups. | |
| Mar 28, 2017 at 10:48 | comment | added | Sebastien Palcoux | @FriederLadisch: do you understand in what sense the (complicated) formula of Pálfy's paper is more interesting than this (easy) formula extracted above? | |
| Mar 27, 2017 at 14:03 | comment | added | Sebastien Palcoux | @FriederLadisch: you are right, thanks! | |
| Mar 27, 2017 at 12:47 | comment | added | Frieder Ladisch | Re "does this theorem exist in the literature?": In Pálfy's paper on p. 97, a chain of equalities is displayed, and from the 1st and the 3rd line, on can extract the equality $$ \sum_{ \substack{ \phi \in \operatorname{Irr}(G) \\ \operatorname{Ker} \phi = 1 } } ( \deg \phi )^2 = \sum_{ N \vartriangleleft G } \mu(N) | G/N|. $$ | |
| Mar 24, 2017 at 23:27 | vote | accept | Sebastien Palcoux | ||
| Mar 24, 2017 at 18:57 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
Definitive answer containing a counter-example, plus an improved question and two counter-examples for it; finally an alternative result involving the normal subgroup lattice, plus a reference request.
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| Mar 24, 2017 at 13:31 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
transfert of the counter-example to the (improved) question part.
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| Mar 23, 2017 at 22:52 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
We add a counter-example, so that it is a real answer (m=no more a long comment). We also suggest a way for improving the question.
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| Mar 11, 2017 at 22:55 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
Definition of the fixed-point subspace, and link for Claim 1.
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| Mar 11, 2017 at 16:32 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
minor edit
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| Mar 11, 2017 at 15:07 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
minor edit
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| Mar 11, 2017 at 14:33 | history | answered | Sebastien Palcoux | CC BY-SA 3.0 |