From 97feedb5c078eef4a24ecf4e535295e31e3e0218 Mon Sep 17 00:00:00 2001
From: Alexander Hulpke <hulpke@math.colostate.edu>
Date: Sun, 10 Apr 2022 10:05:19 -0600
Subject: [PATCH] MinimalGeneratingSet for solvable non-pc groups

---
 lib/grp.gi      | 16 ++++++++--------
 lib/grppcatr.gi | 11 +++--------
 2 files changed, 11 insertions(+), 16 deletions(-)

diff --git a/lib/grp.gi b/lib/grp.gi
index a4fec06df3..f0012f8c62 100644
--- a/lib/grp.gi
+++ b/lib/grp.gi
@@ -107,21 +107,21 @@ end);
 ##
 #M  MinimalGeneratingSet(<G>) . . . . . . . . . . . . . for groups
 ##
-InstallMethod(MinimalGeneratingSet,"solvable group via pc",true,
-  [IsGroup],0,
+InstallMethod(MinimalGeneratingSet,"test solvable and 2-generator noncyclic",
+  true, [IsGroup and IsFinite],0,
 function(G)
 local i;
-  if not IsSolvableGroup(G) then
-    if IsGroup(G) and HasGeneratorsOfGroup(G)
+  if not HasIsSolvableGroup(G) and IsSolvableGroup(G) and
+  CanEasilyComputePcgs(G)  then
+    # discovered solvable -- redo
+    return MinimalGeneratingSet(G);
+  elif not IsSolvableGroup(G) then
+    if IsGroup(G) and (not IsCyclic(G)) and HasGeneratorsOfGroup(G)
         and Length(GeneratorsOfGroup(G)) = 2 then
       return GeneratorsOfGroup(G);
     fi;
     TryNextMethod();
   fi;
-  i:=IsomorphismPcGroup(G);
-  G:=Image(i,G);
-  G:=MinimalGeneratingSet(G);
-  return List(G,j->PreImagesRepresentative(i,j));
 end);
 
 #############################################################################
diff --git a/lib/grppcatr.gi b/lib/grppcatr.gi
index 29c64eb9d3..ef65518680 100644
--- a/lib/grppcatr.gi
+++ b/lib/grppcatr.gi
@@ -612,7 +612,7 @@ end;
 ##
 InstallMethod( MinimalGeneratingSet,
     "pcgs computable groups using special pcgs",
-    true, [ IsPcGroup and IsFinite ], 0,
+    true, [ IsSolvableGroup and IsFinite and CanEasilyComputePcgs], 0,
 
 function( G )
     local spec, weights, first, m, mingens, i, start, next, j,
@@ -662,13 +662,8 @@ end );
 #M  SmallGeneratingSet(<G>) 
 ##
 InstallMethod(SmallGeneratingSet,"using minimal generating set",true,
-  [IsPcGroup and IsFinite],0,
-function (G)
-  if Length(Pcgs(G))>14 then
-    TryNextMethod();
-  fi;
-  return MinimalGeneratingSet(G);
-end);
+  [IsSolvableGroup and IsFinite and CanEasilyComputePcgs],0,
+  MinimalGeneratingSet);
 
 #############################################################################
 ##