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bug in ClassPositionsOfLowerCentralSeries #3321

@ThomasBreuer

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@ThomasBreuer

Frieder Ladisch had reported the following bug:

gap> g:= SmallGroup( 3^5, 22 );;
gap> LowerCentralSeries(g);
[ C27 : C9, Group([ f3, f5 ]), Group([ f5 ]), Group([ <identity> of ... ]) ]
gap> ct:= CharacterTable(g);;
gap> ClassPositionsOfLowerCentralSeries(ct);
[ [ 1 .. 35 ], [ 1, 4, 6, 12, 15 ] ]

Looking at the code, I found related issues:

  • ElementaryAbelianSeries runs into an error if the argument is a nonsolvable group.
    According to the documentation, fail should be returned.
    I think the function should be adjusted to the documentation.
    (The corresponding function ClassPositionsOfElementaryAbelianSeries returns fail
    for character tables of nonsolvable groups.)
  • UpperCentralSeries returns a descending series,
    whereas ClassPositionsOfUpperCentralSeries returns an ascending series.
    The documentation of UpperCentralSeries coincides with the return value.
    Here I am not sure what to do.
  • In order to run a reasonable amount of tests (on small groups) that compare the
    ClassPositionsOf... functions with the corresponding functions for groups,
    it makes sense to improve the code of some ClassPositionsOf... methods.

I will provide a pull request.

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    kind: bugIssues describing general bugs, and PRs fixing themkind: bug: wrong resultIssues describing bugs that result in mathematically or otherwise wrong results, and PRs fixing them

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