Timeline for When does a semisimple $\mathbb{C}$-algebra come from a group?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 24, 2020 at 5:05 | comment | added | Sebastien Palcoux | If $n_1 \le n_2 \le \dots \le n_m$ and $n_2>1$, then $\sum_i n_i^2 \equiv 0 \mod 4$ (it is a property of the non-trivial perfect group). See math.stackexchange.com/q/1357885/84284 | |
| Nov 23, 2020 at 18:22 | comment | added | YCor | Maybe. Actually the other question asks several questions, which leaves less focus on this very question, so I have no definite opinion. | |
| Nov 23, 2020 at 18:20 | comment | added | YCor | Examples of easy necessary conditions: write $n=\sum n_i^2$. Then necessarily $|G|=n$. For many values of $n$ this gives restrictions. For instance, if $n$ is prime, square of prime, or some other values such as $15$, then this is plausible only if all $n_i=1$. If $n\ge 3$ is odd, or of the form $p^aq^b$, $G$ should be solvable, so $n_1$ should be $>1$. | |
| Nov 23, 2020 at 18:19 | comment | added | pitariver | @Ycor I see, I only saw that post from Mare's answer, so should I delete this question as a result (I agree it's a duplicate)? | |
| Nov 23, 2020 at 18:18 | comment | added | YCor | This indeed seems to make a duplicate (I have the gr.group-theory golden badge which would close the question as duplicate from my only vote, so I don't vote). The other question has no accepted answer, probably because we don't really expect a definite answer. | |
| Nov 23, 2020 at 18:17 | history | edited | pitariver | CC BY-SA 4.0 |
changed a sum
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| Nov 23, 2020 at 18:15 | comment | added | Mare | See also mathoverflow.net/questions/314502/… | |
| Nov 23, 2020 at 18:14 | history | edited | pitariver | CC BY-SA 4.0 |
added conditions
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| Nov 23, 2020 at 17:41 | history | asked | pitariver | CC BY-SA 4.0 |