[GAP Forum] Question about SubdirectProduct

[Piotr Jastrzębski]

There is also problem that in first case 'wprod' have more generators 
than 'gamma'.
https://groupprops.subwiki.org/wiki/GAP:IsSubgroup
This function returns true if the second group is a subgroup of the 
first.
Piotr

W dniu 2018-07-24 09:37, Piotr Jastrzębski napisał(a):
> Hi,
> 
> there is some problem with function IsSubgroup when generators of
> objects (eg. groups) are not expressed explicitly. In your example:
> 
> I case
> gap> Display(gamma);
> Group( [ f1, f2, f3, f4, f5, f6, f7, f8 ] )
> gap> Display(wprod);
> Group( [ f1, f2, f3, f4, f5, f6, f7, f8, f9, f10 ] )
> 
> II case
> gap> Display(gamma);
> Group( [ (1,2,3), (1,2)(4,5), (4,5,6) ] )
> gap> Display(wprod);
> Group( [ (1,2,3), (1,2), (4,5,6), (4,5) ] )
> 
> 
> To fix it,
> the function IsSubgroup should be extended with implicit generators
> like f1,..., fn.
> 
> Best Regards,
> Piotr
> 
> 
> 
> 
> W dniu 2018-07-24 05:23, German Combariza napisał(a):
>> Dear all,
>> 
>> I am having problems with the function SubdirectProduct. Looks like
>> GAP does not recognize the SubdirectProduct as a subgroup of the
>> DirectProduct, but It does for small groups.
>> 
>> Example:
>> 
>> s4  := Group((1,2,3,4),(1,2));;
>> list := AllSmallGroups(48);;
>> n := 48;;
>> g := list[n];;
>> hom := AllHomomorphisms(list[n], s4)[53];;
>> gamma := SubdirectProduct(g,g,hom,hom);;
>> wprod := DirectProduct(g,g);;
>> IsSubgroup( wprod, gamma);  # This is False
>> 
>> However:
>> g := Group((1,2,3),(1,2));;
>> k  := Group((1,2));;
>> hom := AllHomomorphisms(g, k)[2];;
>> gamma := SubdirectProduct(g,g,hom,hom);;
>> wprod := DirectProduct(g,g);;
>> IsSubgroup( wprod, gamma);  # This is true.
>> 
>> Thanks!
>> 
>> 
>> 
>> 
>> 
>> 
>> _______________________________________________
>> Forum mailing list
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> 
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