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Add NormalHallSubgroups #561

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merged 1 commit into from
Mar 28, 2016

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hungaborhorvath
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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.

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 fingolfin added the kind: enhancement Label for issues suggesting enhancements; and for pull requests implementing enhancements label Feb 10, 2016
@markuspf markuspf added this to the GAP 4.9.0 milestone Mar 7, 2016
@markuspf markuspf merged commit d59a4db into gap-system:master Mar 28, 2016
@olexandr-konovalov
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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?

@hungaborhorvath
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@alex-konovalov I wrote a sentence about it, is that enough?

@hungaborhorvath hungaborhorvath deleted the NormalHallSubgroups branch April 3, 2016 19:31
@olexandr-konovalov olexandr-konovalov added the release notes: added PRs introducing changes that have since been mentioned in the release notes label Jan 20, 2018
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4 participants