diff --git a/src/sage/groups/abelian_gps/abelian_group_gap.py b/src/sage/groups/abelian_gps/abelian_group_gap.py
index 74bcc74de1e..a4450b53b40 100644
--- a/src/sage/groups/abelian_gps/abelian_group_gap.py
+++ b/src/sage/groups/abelian_gps/abelian_group_gap.py
@@ -365,7 +365,10 @@ def _element_constructor_(self, x, check=True):
                 raise ValueError("input does not match the number of generators")
             x = self.one()
             for i in range(len(exp)):
-                x *= gens_gap[i]**(exp[i] % orders[i])
+                if orders[i] > 0:
+                    x *= gens_gap[i]**(exp[i] % orders[i])
+                else:
+                    x *= gens_gap[i]**exp[i]
             x = x.gap()
         return self.element_class(self, x, check=check)