Timeline for The prime divisors of a simple group
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2012 at 12:37 | answer | added | Jim Humphreys | timeline score: 6 | |
| Apr 6, 2012 at 16:32 | answer | added | John McKay | timeline score: 1 | |
| Apr 6, 2012 at 10:36 | history | edited | Tom De Medts | CC BY-SA 3.0 |
added tag "finite-groups", minor grammar fixes
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| Apr 6, 2012 at 10:01 | comment | added | Geoff Robinson | That sort of number theory might be do-able, but it can't really be classification-free, because you surely need to know there aer only finitely many sporadic simple groups to touch a problem like this, don't you? | |
| Apr 6, 2012 at 8:11 | comment | added | Tom De Medts | I would be surprised if there were a classification-free proof. Just think of how hard it already is to prove that $2 \in \pi(G)$! But even with the classification in hand, I have the impression that the problem involves some hard number-theoretical questions for the groups of Lie type, having to do with getting hold on the prime divisors of expressions of the form $\prod (q^k -1)$. | |
| Apr 6, 2012 at 6:48 | comment | added | Will Sawin | Given the existence of a nontrivial counterexample at $19$, it seems likely that the easiest proofs is just by checking the classification of finite simple groups. Is there any evidence that there might exist a nicer proof? | |
| Apr 5, 2012 at 15:32 | comment | added | Tom De Medts | I've checked all the examples from madore.org/~david/math/simplegroups.html, and it's true for those at least. (The condition $n \geq 23$ is strictly necessary, since the group $^2E_6(4)$ has the same prime spectrum as $A_{19}$.) | |
| Apr 5, 2012 at 15:20 | history | edited | Sara | CC BY-SA 3.0 |
added 13 characters in body
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| Apr 5, 2012 at 15:09 | comment | added | Tom De Medts | I guess you want to rephrase the question as "Is it true that $G$ is an alternating group?". If $n$ is not prime, then $\pi(A_n) = \pi(A_{n-1})$. | |
| Apr 5, 2012 at 15:03 | comment | added | Sara | In my question $A_{n}$ the alternating group on n letters. Thanks | |
| Apr 5, 2012 at 13:28 | history | asked | Sara | CC BY-SA 3.0 |