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Generating all elements of $SL_2(\mathbb{F}_q)$

Group
matrix

asked 2016-09-26 23:01:48 +0100

vukov
147 ●4 ●5 ●14

What is the fastest way to create a set with all elements of $SL_2(\mathbb{F}_q)$ for $q$ some prime power of size about $50$? One way to do it is to find a representative for each conjugacy class and then use the ConjugacyClass method, but this seems inefficient. Is there a better way?

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answered 2016-09-27 00:59:30 +0100

tmonteil
27423 ●31 ●204 ●517 http://wiki.sagemath.o...

You can define your group as follows:

sage: G = SL(2,GF(53))

Then you can get the list of its elements with the list method:

sage: L = G.list()

On my 5+ years old laptop, it takes about 44 seconds.

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Asked: 2016-09-26 23:01:48 +0100

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Last updated: Sep 27 '16

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