Add NormalHallSubgroups #561
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This is the second installment in the series of enhancing StructureDescription. (The first being DirectFactorsOfGroup.) A new global function NormalHalSubgroupFromSylows is introduced, which computes normal Hall subgroups by computing normal closures of all Sylows. An optional second argument "any" is recognized, in which case the function returns the first nontrivial normal Hall subgroup, if exists, and returns fail, otherwise. This will be used for computing semidirect decompositions, because in this situation the Schur-Zassenhaus theorem guarantees a complement. NormalHallSubgroups is a new attribute, which consists of a list of all normal Hall subgroups of a group. This is currently defined only for groups which can compute size for all their subgroups. This check might not be needed, e.g. the function works for DihedralGroup(IsFpGroup, 60), as well. A test file is added.
fingolfin
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kind: enhancement
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@hungaborhorvath: since this PR now merged, could you please add to the Wiki page for the next major release the text to include in the changes manual and the release announcement? |
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@alex-konovalov I wrote a sentence about it, is that enough? |
olexandr-konovalov
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release notes: added
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This is the second installment in the series of enhancing
StructureDescription. (The first being DirectFactorsOfGroup.)
A new global function NormalHalSubgroupFromSylows is introduced, which
computes normal Hall subgroups by computing normal closures of all Sylows.
An optional second argument "any" is recognized, in which case the function
returns the first nontrivial normal Hall subgroup, if exists, and returns
fail, otherwise. This will be used for computing semidirect decompositions,
because in this situation the Schur-Zassenhaus theorem guarantees a
complement.
NormalHallSubgroups is a new attribute, which consists of a list of all
normal Hall subgroups of a group. This is currently defined only for groups
which can compute size for all their subgroups. This check might not be
needed, e.g. the function works for DihedralGroup(IsFpGroup, 60), as well.
A test file is added.