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Constructions in Sage: A Sage cookbook |  |
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Constructions in Sage: A Sage cookbook | |
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If you want to find all the normal subgroups of a permutation
group 
(up to conjugacy), you can use Sage's interface
to GAP:
sage: G = AlternatingGroup( 5 ) sage: gap(G).NormalSubgroups() [ Group( () ), AlternatingGroup( [ 1 .. 5 ] ) ]
or
sage: G = gap("AlternatingGroup( 5 )")
sage: G.NormalSubgroups()
[ Group( () ), AlternatingGroup( [ 1 .. 5 ] ) ]
Here's another way, working more directly with GAP:
sage: print gap.eval("G := AlternatingGroup( 5 )")
Alt( [ 1 .. 5 ] )
sage: print gap.eval("normal := NormalSubgroups( G )")
[ Group(()), Alt( [ 1 .. 5 ] ) ]
sage: G = gap.new("DihedralGroup( 10 )")
sage: G.NormalSubgroups()
[ Group( <identity> of ... ), Group( [ f2 ] ), Group( [ f1, f2 ] ) ]
sage: print gap.eval("G := SymmetricGroup( 4 )")
Sym( [ 1 .. 4 ] )
sage: print gap.eval("normal := NormalSubgroups( G );")
[ Group(()), Group([ (1,4)(2,3), (1,3)(2,4) ]),
Group([ (2,4,3), (1,4)(2,3), (1,3)(2,4) ]), Sym( [ 1 .. 4 ] ) ]
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Constructions in Sage: A Sage cookbook | |
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