To find the (number of) normal subgroups of a group G you use the Filtered command to filter the list of subgroups of G which are normal in G. So if G = D16 is as defined and subs is the list of subgroups of G as defined in the previous post then the command
gap> Filtered( subs, H -> IsNormal( D16, H ) ); will give you the normal subgroups of D16: [ Group([ ]), Group([ f4 ]), Group([ f4, f3 ]), Group([ f4, f3, f1 ]), Group([ f4, f3, f2 ]), Group([ f4, f3, f1*f2 ]), Group([ f4, f3, f1, f2 ]) ] Sandeep > Begin forwarded message: > > From: Murthy Sandeep <sand...@sandeepmurthy.is> > Subject: Re: [GAP Forum] Number of subgroups > Date: 19 April 2015 14:23:40 BST > To: abdulhakeem alayiwola <lovepgro...@gmail.com> > Cc: GAP Forum <fo...@gap-system.org> > > I assume you mean the dihedral group of order 16, so define it: > > gap> D16 := DihedralGroup( 16 ); > <pc group of size 16 with 4 generators> > > and then run the command > > gap> LatticeSubgroups( D16 ); > > which should display > > gap> <subgroup lattice of <pc group of size 16 with 4 generators>, 11 > classes, 19 subgroups> > > This displays information about the lattice of subgroups of D16 using the > conjugacy relation for > subgroups > (http://www.gap-system.org/Manuals/doc/ref/chap39.html#X7FA267497CFC0550). > The classes are the equivalence classes, 11 in this case, and there are 19 > subgroups in total. > > You cannot access the subgroups from the lattice directly (it is not a list > of subgroups), but through > the conjugacy classes. To do this you have to call the > ConjugacyClassesOfSubgroups( <lattice> ) > function with a given lattice, which gives you a list of the classes, and > then flatten that list. So you > could do something like: > > gap> subs := Flat( List( cls, c -> Elements( c ) ) ) ); > [ Group([ ]), Group([ f4 ]), Group([ f1 ]), Group([ f1*f3 ]), Group([ f1*f4 > ]), Group([ f1*f3*f4 ]), Group([ f1*f2 ]), > Group([ f1*f2*f3 ]), Group([ f1*f2*f4 ]), Group([ f1*f2*f3*f4 ]), Group([ > f4, f3 ]), Group([ f4, f1 ]), > Group([ f1*f3, f4 ]), Group([ f4, f1*f2 ]), Group([ f1*f2*f3, f4 ]), Group([ > f4, f3, f1 ]), Group([ f4, f3, f2 ]), > Group([ f4, f3, f1*f2 ]), Group([ f4, f3, f1, f2 ]) ] > > An alternative to finding the number of subgroups is to load the Sonata > package > (http://www.gap-system.org/Packages/sonata.html) using > > gap> LoadPackage( “Sonata” ); > > and then run the command > > gap> Number( Subgroups( D16 ) ); > > which should display 19. > > Sandeep > > >> On 19 Apr 2015, at 11:35, abdulhakeem alayiwola <lovepgro...@gmail.com> >> wrote: >> >> how do i get the number of subgroups of D-16? >> _______________________________________________ >> Forum mailing list >> Forum@mail.gap-system.org >> http://mail.gap-system.org/mailman/listinfo/forum >
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