fix delegations among IrreducibleModules methods (#5925)

* fix delegations among `IrreducibleModules` methods

There were infinite recursions in the case of abelian groups.

Apparently there is code for computing the irreducible representations
of abelian groups over finite fields only for the case of prime fields.

The infinite recursions do not catch the case of non-prime fields
anymore after the current changes; the generic code now runs into
errors.

* hack in order to make more cases work

Once we know that our group is abelian,
call `IrreducibleModules` without restricting the dimension to 1,
and later filter the result in order to take just the 1-dim. modules.
(This is not a good solution, but at least more tests are working now.)

Author: ThomasBreuer

lib/grpreps.gi

@@ -55,20 +55,39 @@ local modu, modus,gens,v,subs,sub,ser,i,j,a,si,dims,cf,mats,clos,bas,rad;
     a:=DerivedSubgroup(G);
     if Size(a)=Size(G) then
       return [gens,[TrivialModule(Length(gens),F)]];
-    else
-      a:=MaximalAbelianQuotient(G);
-      si:=List(gens,x->ImagesRepresentative(a,x));
-      sub:=IrreducibleModules(Group(si),F,1);
-      if sub[1]=si then
-        return [gens,sub[2]];
+    elif IsAbelian(G) then
+      if IsPrimeField(F) then
+        if CanEasilyComputePcgs(G) then
+          # call `IrreducibleMethods` again;
+          # we assume that now another method is applicable
+          return IrreducibleModules(G, F, 1);
+        else
+          # delegate to a pc group,
+          # for which another method is available
+          a:= IsomorphismPcGroup(G);
+        fi;
       else
-        modu:=[];
-        for i in sub[2] do
+        a:= IsomorphismPermGroup(G);
+      fi;
+    else
+      # delegate to a proper factor group
+      a:= MaximalAbelianQuotient(G);
+    fi;
+    si:=List(gens,x->ImagesRepresentative(a,x));
+    sub:= Group(si);
+    SetIsAbelian(sub, true);
+    sub:= IrreducibleModules(sub,F,0);
+    if sub[1]=si then
+      return [gens, Filtered( sub[2], x -> x.dimension = 1 )];
+    else
+      modu:=[];
+      for i in sub[2] do
+        if i.dimension = 1 then
           v:=GroupHomomorphismByImages(Image(a),Group(i.generators),sub[1],i.generators);
           Add(modu,GModuleByMats(List(si,x->ImagesRepresentative(v,x)),F));
-        od;
-        return [gens,modu];
-      fi;
+        fi;
+      od;
+      return [gens,modu];
     fi;
 
   fi;

tst/testinstall/grpreps.tst

@@ -16,5 +16,21 @@ gap> res2:= AbsolutelyIrreducibleModules( G2, F, 10 );;
 gap> List( res2[2], r -> [ r.field, r.dimension ] );
 [ [ GF(2), 1 ] ]
 
+# Test that the delegation between methods for 'IrreducibleModules' works.
+gap> Length( IrreducibleModules( AlternatingGroup(5), GF(3), 1 )[2] ) = 1;
+true
+gap> Length( IrreducibleModules( Group( (1,2), (1,2) ), GF(3), 1 )[2] ) = 2;
+true
+gap> Length( IrreducibleModules( Group( (1,2), (1,2) ), GF(4), 1 )[2] ) = 1;
+true
+gap> Length( IrreducibleModules( Group( (1,2,3,4,5) ), GF(4), 1 )[2] ) = 1;
+true
+gap> Length( IrreducibleModules( CyclicGroup( IsFpGroup, 2 ), GF(3), 1 )[2] ) = 2;
+true
+gap> Length( IrreducibleModules( CyclicGroup( IsFpGroup, 2 ), GF(4), 1 )[2] ) = 1;
+true
+gap> Length( IrreducibleModules( SymmetricGroup(5), GF(3), 1 )[2] ) = 2;
+true
+
 #
 gap> STOP_TEST( "grpreps.tst" );