Timeline for Finite groups such that every irrep can be induced from trivial irrep of a subgroup ?
Current License: CC BY-SA 3.0
14 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Sep 5, 2012 at 14:22 | vote | accept | Alexander Chervov | ||
| Aug 26, 2012 at 22:38 | history | edited | Chris Gerig | CC BY-SA 3.0 |
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| Aug 26, 2012 at 22:31 | answer | added | Will Sawin | timeline score: 24 | |
| Aug 26, 2012 at 22:30 | answer | added | Jim Humphreys | timeline score: 5 | |
| Aug 26, 2012 at 22:26 | comment | added | David E Speyer | Andreas (above) is replying to a comment which I deleted, because I realized that I had misread the question. | |
| Aug 26, 2012 at 22:08 | answer | added | Geoff Robinson | timeline score: 16 | |
| Aug 26, 2012 at 21:49 | comment | added | Will Sawin | A simpler example is $\mathbb Z/4$. An abelian group has this property if and only if it fails to be cyclic. Even $\mathbb Z/2$ fails, for having no proper nontrivial subgroup. | |
| Aug 26, 2012 at 21:33 | comment | added | Andreas Blass | A slight extension of example 2: If $G$ has a smallest non-trivial subgroup (e.g., the quaternion group), then the requirement isn't satisfied. The smallest non-trivial subgroup is a normal subgroup all of whose elements act trivially in all the induced representations that you consider. So you won't get any of the irreps in which elements of this subgroup act nontrivially. | |
| Aug 26, 2012 at 21:30 | comment | added | Andreas Blass | @David: The OP is, if I understand correctly, only asking that each irrep appear as a summand in one of the induced representations. It's OK if there are lots of other summands (like the trivial one) along with it. For example, if $G$ is the Klein four-group, then all 4 irreps occur within the 4 induced reps (in fact, within the 3 non-trivial induced reps). | |
| Aug 26, 2012 at 20:20 | history | edited | Alexander Chervov | CC BY-SA 3.0 |
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| Aug 26, 2012 at 20:18 | comment | added | Alexander Chervov | Subgroup is allowed to vary. Sorry for being unclear about this. I will edit. | |
| Aug 26, 2012 at 20:16 | comment | added | Benjamin Steinberg | Do you want one subgroup to give all the irreducible representations or is the subgroup allowed to vary? | |
| Aug 26, 2012 at 20:13 | history | asked | Alexander Chervov | CC BY-SA 3.0 |