> On 19 Apr 2015, at 06:10, abdulhakeem alayiwola <lovepgro...@gmail.com> wrote: > > how many central automorphism does D-16 have? > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum
The command gap> Order( Centre( AutomorphismGroup( DihedralGroup( 16 ) ) ) ); 2 Sandeep > Begin forwarded message: > > From: Murthy Sandeep <sand...@sandeepmurthy.is> > Subject: Fwd: [GAP Forum] Number of subgroups > Date: 19 April 2015 15:08:32 BST > To: abdulhakeem alayiwola <lovepgro...@gmail.com> > Cc: GAP Forum <fo...@gap-system.org> > > 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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