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How to iterate over groups in increasing size

asked 2016-05-10 15:14:01 -0500

Asvin gravatar image

updated 2016-05-10 15:14:28 -0500

I would like some way to iterate over all finite groups in increasing size till I manually stop the program (preferably as permutation groups). Is there an easy command to do this?

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answered 2016-05-11 07:49:13 -0500

updated 2016-05-11 07:49:40 -0500

In GAPthere are various databases available for groups, see http://www.gap-system.org/Datalib/dat...

Some of them are interfaced in Sage and available in the database_gap package. So first of all you have to install the package with the console command (needs internet connection)

$ sage -i database_gap

Then if you launch Sage you should be able to do

sage: for G in TransitiveGroups():
....:     print G
....:     print G.gens() 
Transitive group number 1 of degree 0
[()]
Transitive group number 1 of degree 1
[()]
Transitive group number 1 of degree 2
[(1,2)]
Transitive group number 1 of degree 3
[(1,2,3)]
Transitive group number 2 of degree 3
[(1,2), (1,2,3)]
Transitive group number 1 of degree 4
[(1,2,3,4)]
...
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Asked: 2016-05-10 15:14:01 -0500

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Last updated: May 11 '16