Timeline for Which finite groups have faithful complex irreducible representations?
Current License: CC BY-SA 2.5
11 events
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| Jul 17, 2015 at 2:38 | comment | added | Nico Bellic | I would like to ask a variation on this question: Characterize finite groups G which admit an irreducible representation in which the group action is free on the compliment of the origin. | |
| Jan 3, 2015 at 12:14 | comment | added | Sebastien Palcoux | Are the distributive permutation groups linearly primitive? | |
| Apr 12, 2011 at 18:50 | answer | added | Rob Harron | timeline score: 13 | |
| Mar 2, 2011 at 18:27 | vote | accept | Fedor Petrov | ||
| Mar 2, 2011 at 18:26 | history | edited | Fedor Petrov | CC BY-SA 2.5 |
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| Mar 2, 2011 at 18:25 | comment | added | Fedor Petrov | I thought about complex numbers, but other fields are of interest too. | |
| Mar 2, 2011 at 17:02 | answer | added | Andreas Thom | timeline score: 30 | |
| Mar 2, 2011 at 17:01 | comment | added | Jim Humphreys | P.S. It's also important here to specify the field or its characteristic, since that affects such existence questions. | |
| Mar 2, 2011 at 16:53 | history | edited | Fedor Petrov | CC BY-SA 2.5 |
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| Mar 2, 2011 at 16:52 | comment | added | Jim Humphreys |
I'm assuming that "exact" here means "faithful" (representation has trivial kernel). For finite $p$-groups, it's a standard fact that having a faithful irreducible representation is equivalent to having a cyclic center. I'm not sure about the general case, but it's been discussed in many books and papers. My impression is that there is no known definitive structural condition for sufficiency.
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| Mar 2, 2011 at 16:41 | history | asked | Fedor Petrov | CC BY-SA 2.5 |