If one wants to store a large number of pc groups, then it can be useful to store them in a compressed format, since pc presentations can be space consuming. Here we introduce a method to code and decode pc presentations by integers. To decode a given code the size of the underlying pc group is needed as well. For the full definition and the coding and decoding procedures see BescheEick98. This method is used with the small groups library, see Section Small Groups.
CodePcgs( pcgs ) F
returns the code corresponding to pcgs.
CodePcGroup( G ) F
returns the code for a pcgs of G.
PcGroupCode( code, size ) F
returns a pc group of size size corresponding to code.
PcGroupCodeRec( rec ) F
Here rec needs to have entries .code and .order. Then PcGroupCode returns a pc group of size .order corresponding to .code.
gap> G := SmallGroup( 24, 12 );; gap> p := Pcgs( G );; gap> code := CodePcgs( p ); 5790338948 gap> H := PcGroupCode( code, 24 ); <pc group of size 24 with 4 generators> gap> map := GroupHomomorphismByImages( G, H, p, FamilyPcgs(H) ); Pcgs([ f1, f2, f3, f4 ]) -> Pcgs([ f1, f2, f3, f4 ]) gap> IsBijective(map); true
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GAP 4 manual