Dear Alex & forum, I want to offer a naive solution to your question. I hope that more experienced users will "chip in" to improve it.
Best wishes, Stefanos #Check whether a group is quasi-simple, i.e., perfect whose quotient by its centre is (non-abelian) simple IsQuasisimpleGroup:=function(g) local quo; if IsSolvableGroup(g) then return false; fi; if IsPerfectGroup(g) then quo:=FactorGroup(g,Center(g)); if IsSimpleGroup(quo) then return true; fi; fi; return false; end;; #Construct the layer of a group, that is, the product of its subnormal quasi-simple subgroups Layer:=function(g) local list,h,lay; if IsSolvableGroup(g) then return TrivialSubgroup(g); fi; if IsSimpleGroup(g) then return g; fi; list:=[];; for h in AllSubgroups(g) do if IsSubnormal(g,h) then if IsQuasisimpleGroup(h) then Append(list,[h]); fi; fi; od; lay:=TrivialSubgroup(g); for h in list do lay:=ClosureGroup(lay,h); od; return lay; end;; #Finally, construct the generalised Fitting subgroup of the group GeneralizedFittingSubgroup:=function(g) local fitt, lay; fitt:=FittingSubgroup(g); lay:=Layer(g); return ClosureGroup(fitt,lay); end;; On 6 January 2018 at 22:02, Alex Trofimuk <trof1...@rambler.ru> wrote: > Dear Forum, > Alex Trofimuk asked: > Whether exists in GAP a function for finding a generalized Fitting > subgroup for > an arbitrary group? > _______________________________________________ > Forum mailing list > Forum@gap-system.org > https://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
