The order in FreeAbelianGroup is broken and makes the domain unusable (e.g., comparison of Set FreeAbelianGroup S does not work properly) For example here is a cycle:

  ----------------------------------------
  Z2:=FreeAbelianGroup Symbol         

  a:= a::FreeAbelianGroup Symbol         
  b:= b::FreeAbelianGroup Symbol
  z:= 0::FreeAbelianGroup Symbol

  a < -b 
  -b < z
  z < a
  ----------------------------------------

thus

(1) -> a:= a::FreeAbelianGroup Symbol         

   There are no library operations named FreeAbelianGroup 
      Use HyperDoc Browse or issue
                          )what op FreeAbelianGroup
      to learn if there is any operation containing " FreeAbelianGroup 
      " in its name.

   Cannot find a definition or applicable library operation named 
      FreeAbelianGroup with argument type(s) 
                                    Type

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

proposed patch in the last few lines of free.spad:

  545,546c545,546
  <         ta.gen < tb.gen => true
  <         ta.gen > tb.gen => false
  ---
  >         ta.gen < tb.gen => tb.exp > 0
  >         ta.gen > tb.gen => ta.exp < 0

apparently revlex order is intended but is not achieved in the current implementation, as the sign of the trailing exponent is not taken into account.