Minimal Permutation Degree for Simple and Semi-Simple Groups #5732
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,129 @@ | ||
| gap> START_TEST("MinimalFaithfulPermutationDegreeOfSimpleGroup.tst"); | ||
| gap> checksimple := function(maxsize) | ||
| > local i,mu,mu2,info,G; | ||
| > i := 1; | ||
| > for G in SimpleGroupsIterator(1,maxsize) do | ||
| > mu := DoMinimalFaithfulPermutationDegree(G,false); | ||
| > mu2 := MinimalFaithfulPermutationDegreeOfSimpleGroup(G); | ||
| > if mu2 <> mu then | ||
| > info := IsomorphismTypeInfoFiniteSimpleGroup(G); | ||
| > return Concatenation("Failed on simple group ",String(i)," i.e. ",info.name,"\n"); | ||
| > fi; | ||
| > i := i + 1; | ||
| > od; | ||
| > return "Passed"; | ||
| > end; | ||
| function( maxsize ) ... end | ||
| gap> checksimple(50000); # first 26 simple groups | ||
| "Passed" | ||
| gap> Clean := function(INFO) | ||
| > local SporNames,SeriesNames,info,name,q,size; | ||
| > info := ShallowCopy(INFO); | ||
| > SporNames := [ | ||
| > ["M11","M(11)"], | ||
| > ["M12","M(12)"], | ||
| > ["M22","M(22)"], | ||
| > ["M23","M(23)"], | ||
| > ["M24","M(24)"], | ||
| > ["J1","J(1)"], | ||
| > ["J2","J(2)"], | ||
| > ["J3","J(3)"], | ||
| > ["Co2","Co(2)"], | ||
| > ["Co3","Co(3)"], | ||
| > ["Fi22","Fi(22)"], | ||
| > ]; | ||
| > SeriesNames := [ | ||
| > ["U","2A"], | ||
| > ["S","C"], | ||
| > ["Sz","2B"], | ||
| > ["O+","D"], | ||
| > ["O-","2D"], | ||
| > ["O","B"], | ||
| > ]; | ||
| > if IsString(info[3]) then | ||
| > for name in SporNames do | ||
| > if name[2] = info[3] then | ||
| > info[3] := name[1]; | ||
| > fi; | ||
| > od; | ||
| > if info[3] = "T" then | ||
| > info[2] := "2F"; | ||
| > info[3] := 2; | ||
| > info[4] := 0; | ||
| > fi; | ||
| > else | ||
| > for name in SeriesNames do | ||
| > if name[1] = info[2] then | ||
| > info[2] := name[2]; | ||
| > fi; | ||
| > if INFO[2] = "U" then info[3] := INFO[3] -1;fi; | ||
| > if INFO[2] in ["S","O+","O-"] then info[3] := INFO[3]/2; fi; | ||
| > if INFO[2] = "O" then info[3] := (INFO[3] -1)/2; fi; | ||
| > if not IsInt(info[3]) then Error("wierd .. ",INFO,"\n"); fi; | ||
| > if info[2] = "R" then | ||
| > q := info[3]; | ||
| > size := info[1]; | ||
| > if size = q^3 * (q^3 + 1) * (q-1) and PrimeDivisors(q) = [3] then | ||
| > info[2] := "2G"; | ||
| > elif size = q^12 * (q^6 + 1) * (q^4 -1) * (q^3+1) * (q-1) | ||
| > and PrimeDivisors(q) = [2] then | ||
| > info[2] := "2F"; | ||
| > else | ||
| > Error("Couldn't identify"); | ||
| > fi; | ||
| > fi; | ||
| > od; | ||
| > fi; | ||
| > return info; | ||
| > end; | ||
| function( INFO ) ... end | ||
| gap> MakeRecord := function(INFO) | ||
| > local info,parameter,series,shortname; | ||
| > if IsString(INFO[3]) then | ||
| > return rec( | ||
| > series := "Spor", | ||
| > parameter := INFO[4], | ||
| > shortname := INFO[3], | ||
| > ); | ||
| > fi; | ||
| > if INFO[4] = 0 then | ||
| > parameter := INFO[3]; | ||
| > else | ||
| > parameter := [INFO[3],INFO[4]]; | ||
| > fi; | ||
| > return rec( | ||
| > series := INFO[2], | ||
| > parameter := parameter, | ||
| > ); | ||
| > end; | ||
| function( INFO ) ... end | ||
| gap> LightChecknonabelianSimple := function(perfectTill) | ||
| > local size,series,INFO,G,mu,mu2,mu3,info; | ||
| > for INFO in SIMPLEGPSNONL2 do | ||
| > if LENGTH(INFO) <> 5 then continue; fi; | ||
| > size := INFO[1]; | ||
| > series := INFO[2]; | ||
| > mu := Last(INFO); | ||
| > info := MakeRecord(Clean(INFO)); | ||
| > mu2 := MinimalFaithfulPermutationDegreeOfSimpleGroupWithIsomorphismType(info); | ||
| > if mu < mu2 then | ||
| > return Concatenation("failed on",String(INFO),". From table :",String(mu),", Computed :",String(mu2),"\n"); | ||
| > elif size <= perfectTill and mu>mu2 then | ||
| > if IsString(INFO[3]) then | ||
| > G := SimpleGroup(INFO[3]); | ||
| > elif INFO[4] = 0 then | ||
| > G := SimpleGroup(INFO[2],INFO[3]); | ||
| > else | ||
| > G := SimpleGroup(INFO[2],INFO[3],INFO[4]); | ||
| > fi; | ||
| > mu3 := DoMinimalFaithfulPermutationDegree(G,false); | ||
| > if mu2 <> mu3 then | ||
| > return Concatenation("failed on",String(INFO),". From MinimalFaithfulPermutationDegree :",String(mu3),", Computed :",String(mu2),"\n"); | ||
| > fi; | ||
| > fi; | ||
| > od; | ||
| > return "PASS"; | ||
| > end; | ||
| function( perfectTill ) ... end | ||
| gap> LightChecknonabelianSimple(10^6); | ||
| "PASS" |
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I would prefer to move all of this into
DataAboutSimpleGroup, which already stores a lot of knowledge about the simple groups, if only to keep this data together. The case distinctions for the different classes of groups are already coded there.As that function can take a group as argument, it implies that the global function
MinimalFaithfulPermutationDegreeOfSimpleGroupWithIsomorphismTypewould not be needed.