[GAP Forum] Question about SubdirectProduct

[Piotr Jastrzębski]

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!
> 
> 
> 
> 
> 
> 
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