Timeline for Faithful characters of finite groups
Current License: CC BY-SA 2.5
6 events
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| Mar 17, 2010 at 2:57 | comment | added | Guillermo Mantilla | I was afraid you were going to say that about the triangle inequality, and I sort of see your point. Now, from the point of view of a number theorist $\mathbb{Q}_p$'s -where $p$ includes $\infty$- are just algebraic entities that are attached to the arithmetic of $\mathbb{Q}$. Now for some, $\Z_p$ might be a very analytical object and for some others like me it is an algebraic one. In particular, Cauchy-Schwarz inequality on $\bar{Q}_p$ is an algebraic phenomenon for me while it is not for you. | |
| Mar 16, 2010 at 12:56 | comment | added | darij grinberg | Well, the triangle inequality is not quite algebraic in my opinion ;) - in fact, the problem is that you use the fundamental theorem of algebra, which is analysis (despite the name). Most proofs that use complex numbers would work well in an abstract field extension of Q, but here you explicitly use that the roots of unity lie in C. | |
| Mar 15, 2010 at 0:09 | history | edited | Guillermo Mantilla | CC BY-SA 2.5 |
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| Mar 14, 2010 at 15:47 | comment | added | darij grinberg | I would really like to know a non-analysis proof of this fact. Or, better, the more general fact that the arithmetic mean of some roots of unity is an algebraic integer if and only if these roots are either all equal or the arithmetic mean is zero. | |
| Mar 14, 2010 at 4:38 | history | edited | Guillermo Mantilla | CC BY-SA 2.5 |
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| Mar 14, 2010 at 4:32 | history | answered | Guillermo Mantilla | CC BY-SA 2.5 |