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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