Add some tests for {Fitting,Frattini}Subgroup

tst/testinstall/opers/FittingSubgroup.tst

@@ -0,0 +1,35 @@
+gap> START_TEST("FittingSubgroup.tst");
+
+gap> G:=SylowSubgroup(SymmetricGroup(5),2);;
+gap> HasIsNilpotentGroup(G);
+true
+gap> IsIdenticalObj(G, FittingSubgroup(G));
+true
+gap> G := CyclicGroup(IsPermGroup, 12);;
+gap> IsIdenticalObj(G, FittingSubgroup(G));
+true
+gap> G := CyclicGroup(IsPcGroup, 12);;
+gap> IsIdenticalObj(G, FittingSubgroup(G));
+true
+gap> g := SL(2,5);;
+gap> f := FrattiniSubgroup(g);
+<group of 2x2 matrices of size 2 over GF(5)>
+gap> HasIsNilpotentGroup(f);
+true
+gap> p := SylowSubgroup(g, 2);;
+<group of 2x2 matrices of size 8 over GF(5)>
+gap> HasIsNilpotentGroup(p);
+true
+gap> HasIsNilpotentGroup(FrattiniSubgroup(p));
+true
+gap> g := SL(IsPermGroup,2,5);;
+gap> f := FrattiniSubgroup(g);;
+gap> HasIsNilpotentGroup(f);
+true
+gap> p := SylowSubgroup(g, 2);;
+gap> HasIsNilpotentGroup(p);
+true
+gap> HasIsNilpotentGroup(FrattiniSubgroup(p));
+true
+
+gap> STOP_TEST("FittingSubgroup.tst", 1);

tst/testinstall/opers/FrattiniSubgroup.tst

@@ -0,0 +1,18 @@
+gap> START_TEST("FrattiniSubgroup.tst");
+gap> FrattiniSubgroup(SymmetricGroup(3));
+Group(())
+gap> FrattiniSubgroup(SymmetricGroup(4));
+Group(())
+gap> FrattiniSubgroup(SymmetricGroup(5));
+Group(())
+gap> FrattiniSubgroup(CyclicGroup(IsPermGroup, 3));
+Group(())
+gap> FrattiniSubgroup(CyclicGroup(IsPermGroup, 9));
+Group([ (1,4,7)(2,5,8)(3,6,9) ])
+gap> FrattiniSubgroup(CyclicGroup(IsPcGroup, 3));
+Group([  ])
+gap> FrattiniSubgroup(CyclicGroup(IsPcGroup, 9));
+Group([ f2 ])
+gap> List([1..13],i->Size(FittingSubgroup(SmallGroup(60,i))));
+[ 30, 30, 30, 60, 1, 15, 15, 15, 20, 30, 30, 30, 60 ]
+gap> STOP_TEST("FrattiniSubgroup.tst", 1);