Merge PR #905: Some improvements for LatticeByCyclicExtension

Fixes a bug in LatticeByCyclicExtension, and makes it faster in some cases. Also adds a test.

lib/grp.gi

@@ -62,12 +62,33 @@ InstallMethod( IsCyclic,
  fi;
  end );
 
+InstallMethod( Size,
+ "for a cyclic group",
+ [ IsGroup and IsCyclic and HasGeneratorsOfGroup ],
+ -RankFilter(HasGeneratorsOfGroup),
+function(G)
+ local gens;
+ if HasMinimalGeneratingSet(G) then
+ gens:=MinimalGeneratingSet(G);
+ else
+ gens:=GeneratorsOfGroup(G);
+ fi;
+ if Length(gens) = 1 and gens[1] <> One(G) then
+ SetMinimalGeneratingSet(G,gens);
+ return Order(gens[1]);
+ elif Length(gens) <= 1 then
+ SetMinimalGeneratingSet(G,[]);
+ return 1;
+ fi;
+ TryNextMethod();
+end);
+
 InstallMethod( MinimalGeneratingSet,"cyclic groups",true,
  [ IsGroup and IsCyclic and IsFinite ],
  RankFilter(IsFinite and IsPcGroup),
 function ( G )
 local g;
- if Size(G)=1 then return [];fi;
+ if IsTrivial(G) then return []; fi;
  g:=Product(IndependentGeneratorsOfAbelianGroup(G),One(G));
  Assert( 1, Index(G,Subgroup(G,[g])) = 1 );
  return [g];
@@ -387,9 +408,9 @@ InstallMethod( IsNilpotentGroup,
 #M IsPerfectGroup( <G> ) . . . . . . . . . . . . test if a group is perfect
 ##
 InstallImmediateMethod( IsPerfectGroup,
- IsGroup and IsSolvableGroup and HasSize,
+ IsSolvableGroup and HasIsTrivial,
  0,
- grp -> Size( grp ) = 1 );
+ IsTrivial );
 
 InstallMethod( IsPerfectGroup,
  "method for finite groups",

lib/grplatt.gi

@@ -51,16 +51,22 @@ function (G,func)
 local zuppos, # set of zuppos,result
  c, # a representative of a class of elements
  o, # its order
+ h, # the subgroup < c > of G
  N, # normalizer of < c >
  t; # loop variable
 
+ if HasZuppos(G) then
+ return Filtered(Zuppos(G), c -> func(Subgroup(G,[c])));
+ fi;
+
  # compute the zuppos
  zuppos:=[One(G)];
  for c in List(ConjugacyClasses(G),Representative) do
  o:=Order(c);
- if func(Group(c)) and IsPrimePowerInt(o) then
+ h:=Subgroup(G,[c]);
+ if IsPrimePowerInt(o) and func(h) then
  if ForAll([2..o],i -> Gcd(o,i) <> 1 or not c^i in zuppos) then
- N:=Normalizer(G,Subgroup(G,[c]));
+ N:=Normalizer(G,h);
  for t in RightTransversal(G,N) do
  Add(zuppos,c^t);
  od;
@@ -290,7 +296,7 @@ local G, # group
  G:=arg[1];
  noperf:=false;
  zuppofunc:=false;
- if Length(arg)>1 and IsFunction(arg[2]) then
+ if Length(arg)>1 and (IsFunction(arg[2]) or IsList(arg[2])) then
  func:=arg[2];
  Info(InfoLattice,1,"lattice discarding function active!");
  if IsList(func) then

tst/testinstall/opers/LatticeByCyclicExtension.tst

@@ -0,0 +1,20 @@
+gap> START_TEST("LatticeByCyclicExtension.tst");
+
+#
+gap> G:=SmallGroup(625,1);
+<pc group of size 625 with 4 generators>
+gap> A:=AutomorphismGroup(G);
+<group of size 500 with 7 generators>
+gap> fun:=g->IsInt(4/Size(g));;
+gap> LatticeByCyclicExtension(A);
+<subgroup lattice of <group of size 500 with 7 generators>, 12 classes, 
+12 subgroups>
+gap> LatticeByCyclicExtension(A, fun);
+<subgroup lattice of <group of size 500 with 7 generators>, 3 classes, 
+3 subgroups, restricted under further condition l!.func>
+gap> LatticeByCyclicExtension(A, [fun,fun]);
+<subgroup lattice of <group of size 500 with 7 generators>, 3 classes, 
+3 subgroups, restricted under further condition l!.func>
+
+#
+gap> STOP_TEST("LatticeByCyclicExtension.tst", 1);