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FIX: wreath product with trivial group contains trivial generators #5826

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FriedrichRober
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Generators of wreath products should not contain the identity element, unless the group is trivial.

Text for release notes

see title

Further details

gap> WreathProduct(SymmetricGroup(3), Group( () ));
Group([ (1,2,3), (1,2), () ])

Generators should not contain the identity element,
unless the group is trivial.
@FriedrichRober FriedrichRober added the kind: quirk Issues that are not bugs, but a discrepancy between user expectation and system behavior label Oct 24, 2024
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@fingolfin fingolfin left a comment

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In how far is this a bug that needs "fixing"? I mean, it seems unhelpful and redundant, but not wrong as such?

fi;
# generators for the cases where one component is trivial
if IsTrivial(A) and IsTrivial(B) then
g := Group( One(A) );
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How about just

Suggested change
g := Group( One(A) );
g := A:

or if one really wants a new group:

Suggested change
g := Group( One(A) );
g := TrivialSubgroup( A );

Comment on lines +625 to +626
gens1 := [ One(G) ];
basegens := ShallowCopy(gens1);
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Does taking an empty list here not work?

@fingolfin
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ping @FriedrichRober

@fingolfin
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@FriedrichRober last call for GAP 4.14 ...

@FriedrichRober
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Oh my sincere apologies, I was swallowed in other work and forgot about it.

In how far is this a bug that needs "fixing"? I mean, it seems unhelpful and redundant, but not wrong as such?

You are right. I thought it was breaking something in my package WPE, but actually the bug was hidden somewhere else. Nevertheless, I already have put some work into it, so I wanted to finish cleaning up the redundant generators.

This being said, if it doesn’t make it into 4.14, it’s not a huge deal, since it isn’t a breaking bug. I will try to make it in time though.

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