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#############################################################################
##
#W small.gd GAP group library Hans Ulrich Besche
## Bettina Eick, Eamonn O'Brien
##
Revision.small_gd :=
"@(#)$Id: small.gd,v 4.22 2000/01/18 11:30:06 gap Exp $";
#############################################################################
##
## tell GAP about the component
##
DeclareComponent("small","2.0");
InfoIdgroup := NewInfoClass( "InfoIdgroup" );
UnbindGlobal( "SMALL_AVAILABLE" );
#############################################################################
##
#F SMALL_AVAILABLE( size )
##
## returns fail if the library of groups of <size> is not installed.
## Otherwise a record with some information about the construction of the
## groups of <size> is returned.
DeclareGlobalFunction( "SMALL_AVAILABLE" );
UnbindGlobal( "SmallGroup" );
#############################################################################
##
#F SmallGroup(<size>,<i>)
#F SmallGroup([<size>,<i>])
##
## returns the <i>-th group of order <size> in the catalogue. The group will
## be given as PcGroup, if it is solvable and as permutation group otherwise.
## If the groups of order <size> are not installed, the function returns an
## error.
DeclareGlobalFunction( "SmallGroup" );
#############################################################################
##
#F SelectSmallGroups( argl, all, id )
##
## universal function for 'AllGroups', 'OneGroup' and
## 'IdsOfAllGroups'.
DeclareGlobalFunction( "SelectSmallGroups" );
UnbindGlobal( "AllGroups" );
#############################################################################
##
#F AllSmallGroups( arg )
#F AllGroups( arg )
##
## returns all small groups with certain properties. The first selection
## function has to be `Size'. There are precomputed listings for the
## properties `IsAbelian', `IsNilpotentGroup', `IsSupersolvableGroup',
## `IsSolvableGroup', `RankPGroup', `PClassPGroup', `LGLength',
## `FrattinifactorSize' and `FrattinifactorId' for the groups of order
## at most $1000$ except $512$ and $768$ whose order have more than
## three prime factors.
AllSmallGroups := function( arg )
return SelectSmallGroups( arg, true, false );
end;
DeclareSynonym( "AllGroups", AllSmallGroups );
UnbindGlobal( "OneGroup" );
#############################################################################
##
#F OneSmallGroup( arg )
#F OneGroup( arg )
##
## see `AllSmallGroups'.
OneSmallGroup := function( arg )
return SelectSmallGroups( arg, false, false );
end;
DeclareSynonym( "OneGroup", OneSmallGroup );
UnbindGlobal( "IdsOfAllGroups" );
#############################################################################
##
#F IdsOfAllSmallGroups( arg )
#F IdsOfAllGroups( arg )
##
## similar to `AllGroups' but returns id's instead of groups. This may
## be useful to avoid workspace overflows, if a large number of groups are
## expected in the output.
IdsOfAllGroups := function( arg )
return SelectSmallGroups( arg, true, true );
end;
DeclareSynonym( "IdsOfAllSmallGroups", IdsOfAllGroups );
UnbindGlobal( "NumberSmallGroups" );
#############################################################################
##
#F NumberSmallGroups(<size>)
#F NrSmallGroups(<size>)
##
## returns the number of groups of order <size>.
DeclareGlobalFunction( "NumberSmallGroups" );
DeclareSynonym( "NrSmallGroups",NumberSmallGroups );
#############################################################################
##
#F UnloadSmallGroupsData( )
##
## while GAP loads all necessary data from the small groups library
## automatically, it does not remove the data from the workspace again.
## Usually, this will be not necessary, since the data is stored in
## a compressed format. However, if a large number of small groups have
## been loaded by a user, then the user might wish to remove the
## data from the workspace and this can be done by the above function
## call. Note that this is not dangerous in any case, since the data
## will be reloaded automatically, if necessary.
DeclareGlobalFunction( "UnloadSmallGroupsData" );
UnbindGlobal( "ID_AVAILABLE" );
#############################################################################
##
#F ID_AVAILABLE( size )
##
## returns false, if the identification routines for of groups of <size> is
## not installed. Otherwise a record with some information about the
## identification of groups of <size> is returned.
DeclareGlobalFunction( "ID_AVAILABLE" );
UnbindGlobal( "IdGroup" );
#############################################################################
##
#A IdGroup(<G>)
##
## returns the catalogue number of <G>; that is, the function returns
## a pair `[<size>, <i>]' meaning that <G> is isomorphic to
## `SmallGroup( <size>, <i> )'.
DeclareAttribute( "IdGroup", IsGroup );
UnbindGlobal( "Gap3CatalogueIdGroup" );
#############################################################################
##
#F SmallGroupsInformation( size )
##
## prints information on the groups of the specified size.
DeclareGlobalFunction( "SmallGroupsInformation" );
#############################################################################
##
#A Gap3CatalogueIdGroup(<G>)
##
## returns the catalogue number of <G> in the GAP 3 catalogue of solvable
## groups; that is, the function returns a pair `[<size>, <i>]' meaning that
## <G> is isomorphic to the group `SolvableGroup( <size>, <i> )' in GAP 3.
DeclareAttribute( "Gap3CatalogueIdGroup", IsGroup );
#############################################################################
##
#F Gap3CatalogueGroup(<size>,<i>)
##
## returns the <i>-th group of order <size> in the GAP 3 catalogue of
## solvable groups. This group is isomorphic to the group returned by
## `SolvableGroup( <size>, <i> )' in GAP 3.
DeclareGlobalFunction( "Gap3CatalogueGroup" );
#############################################################################
##
#A FrattinifactorSize(<G>)
##
DeclareAttribute( "FrattinifactorSize", IsGroup );
#############################################################################
##
#A FrattinifactorId( <G> )
##
DeclareAttribute( "FrattinifactorId", IsGroup );
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