Don't know

gap/semigroups/semicons.gd

@@ -20,6 +20,8 @@ DeclareGlobalFunction("LeftZeroSemigroup");
 DeclareGlobalFunction("RightZeroSemigroup");
 DeclareConstructor("BrandtSemigroupCons", [IsSemigroup, IsGroup, IsPosInt]);
 DeclareGlobalFunction("BrandtSemigroup");
+DeclareConstructor("FreeSemilatticeCons", [IsSemigroup, IsPosInt]);
+DeclareGlobalFunction("FreeSemilattice");
 
 DeclareCategory("IsSSSE", IsAssociativeElement);
 DeclareCategoryCollections("IsSSSE");

gap/semigroups/semicons.gi

@@ -718,7 +718,7 @@ function(arg)
     S := BrandtSemigroupCons(arg[1], arg[2], arg[3]);
   else
     ErrorNoReturn("the arguments must be a positive integer or a filter and",
-                   " a positive integer, or  a perm group and positive ",
+                   " a positive integer, or a perm group and positive ",
                    "integer, or a filter, perm group, and positive ",
                    "integer");
   fi;
@@ -796,6 +796,26 @@ for _IsXSemigroup in ["IsTransformationSemigroup",
 od;
 Unbind(_IsXSemigroup);
 
+InstallGlobalFunction(FreeSemilattice,
+function(arg)
+  local S;
+
+  if Length(arg) = 0 then
+    S := TrivialSemigroupCons(IsTransformationSemigroup, 0);
+  elif Length(arg) = 1 and IsInt(arg[1]) and arg[1] >= 0 then
+    S := TrivialSemigroupCons(IsTransformationSemigroup, arg[1]);
+  elif Length(arg) = 1 and IsOperation(arg[1]) then
+    S := TrivialSemigroupCons(arg[1], 0);
+  elif Length(arg) = 2 and IsOperation(arg[1]) and IsInt(arg[2])
+      and arg[2] >= 0 then
+    S := TrivialSemigroupCons(arg[1], arg[2]);
+  else
+    ErrorNoReturn("the arguments must be a non-negative integer or ",
+                  "a filter and a non-negative integer");
+  fi;
+  SetIsTrivial(S, true);
+  return S;
+end);
 InstallMethod(StrongSemilatticeOfSemigroups,
 "for a digraph, a list, and a list",
 [IsDigraph, IsList, IsList],

gap/semigroups/semiex.gi

@@ -1,7 +1,7 @@
 #############################################################################
 ##
 ##  semigroups/semiex.gi
-##  Copyright (C) 2013-2022                               James D. Mitchell
+##  Copyright (C) 2013-2023                              James D. Mitchell
 ##
 ##  Licensing information can be found in the README file of this package.
 ##