fix IsomorphismPermGroup for trivial f. p. (sub)group (#6170)

Author: ThomasBreuer

lib/grpfp.gi

@@ -4017,7 +4017,7 @@ local mappow, G, max, p, gens, rels, comb, i, l, m, H, HH, t, sz,
     max:=CosetTableDefaultMaxLimit;
   fi;
 
-  # handle free and trivial group
+  # handle trivial free group
   if 0 = Length( FreeGeneratorsOfFpGroup( G )) then
     p:=GroupHomomorphismByImagesNC(G,GroupByGenerators([],()),[],[]);
     SetIsomorphismPermGroup(G,p);
@@ -4056,12 +4056,16 @@ local mappow, G, max, p, gens, rels, comb, i, l, m, H, HH, t, sz,
     fi;
     SetSize(G,sz);
   fi;
-  if Size(G)=infinity then
+  sz:= Size(G);
+  if sz = infinity then
     return fail;
+  elif sz = 1 then
+    # handle trivial group
+    p:= GroupHomomorphismByImagesNC( G, GroupByGenerators( [], () ), [], [] );
+    SetIsomorphismPermGroup( G, p );
+    return p;
   fi;
 
-  sz:=Size(G);
-
   if sz*10>max then
     max:=sz*10;
   fi;

tst/testinstall/grpfp.tst

@@ -1,4 +1,4 @@
-#@local a,b,c2,e,f,g,iter,l,s,F,rels,sub,iso,G,hom,m
+#@local a,b,c2,e,f,g,iter,l,s,F,rels,sub,iso,G,hom,m,H
 gap> START_TEST("grpfp.tst");
 gap> f:= FreeGroup( "a", "b" );;  a := f.1;;  b := f.2;;
 gap> c2:= f / [ a*b*a^-2*b*a/b, (b^-1*a^3*b^-1*a^-3)^2*a ];;
@@ -177,5 +177,14 @@ gap> ReducedForm(F,UnderlyingElement(
 > Product(GeneratorsOfMonoid(m){[1,3..19]})));
 b2*b4*w1*b1*b6*b8*b9
 
+#
+gap> F:= FreeGroup( 1 );;
+gap> G:= F / [ F.1 ];;
+gap> H:= Subgroup( G, [ G.1 ] );;
+gap> IsomorphismPermGroup( G ) <> fail;
+true
+gap> IsomorphismPermGroup( H ) <> fail;
+true
+
 #
 gap> STOP_TEST( "grpfp.tst" );