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I want to find the elements of the Alternating group of some largest degree, but when I try

g:=Elements(AlternatingGroup(31));

it always gives an error of exceeded the permitted memory. Is there anyway to check the elements of the altenating group of largest degree?

S786
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  • yes, I have to find the length of every element of the group which has some certain properties. To test those it is compulsory to find first elements of group. – S786 Jan 19 '15 at 16:31
  • For instance, if I have to find the element of the group of prime cycle. How can I without knowing the elements of the group. – S786 Jan 19 '15 at 16:33
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    The fastest computers with thousands of processors would take months or years to do this. I suspect you don't have to do an exhaustive search to accomplish what you're trying to do. – Matt Samuel Jan 19 '15 at 16:39
  • I think I should check the conjugacy classes of the group then try to find the length of their representatives as Alexander told me once. – S786 Jan 19 '15 at 16:50

1 Answers1

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Presumably (from the comments) you are looking for the largest order. The GAP command to do so from class representative would be (for a group $G$):

 Maximum(List(ConjugacyClasses(G),x->Order(Representative(x)));

but for the alternating groups of course this either can be calculated from partitions

par:=Filtered(Partitions(31),x->IsEvenInt(Number(x,y->IsEvenInt(y))));;
Maximum(List(par,Lcm));

or even looked up in OEIS: https://oeis.org/A051593 .

ahulpke
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    This GAP 4 Tutorial from ISSAC 2000 by @ahulpke may contain some outdated numbers, as GAP made a step forward since that, but many hints like those in Section called "Harder Problems" will remain fundamental for computational approaches at any time, and I'd very much recommend to read this tutorial (perhaps Alexander could point out to a newer text on this). – Olexandr Konovalov Jan 19 '15 at 20:39