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

a:= a::FreeAbelianGroup Symbol

(1)

Type: FreeAbelianGroup(Symbol)

b:= b::FreeAbelianGroup Symbol

(2)

Type: FreeAbelianGroup(Symbol)

z:= 0::FreeAbelianGroup Symbol

(3)

Type: FreeAbelianGroup(Symbol)

(a < -b)::Boolean

(4)

Type: Boolean

(-b < z)::Boolean

(5)

Type: Boolean

(z < a)::Boolean

(6)

Type: Boolean

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.