diff --git a/src/sage/groups/cubic_braid.py b/src/sage/groups/cubic_braid.py
index e407b9d1326..db826937103 100644
--- a/src/sage/groups/cubic_braid.py
+++ b/src/sage/groups/cubic_braid.py
@@ -640,7 +640,6 @@ class CubicBraidGroup(UniqueRepresentation, FinitelyPresentedGroup):
         sage: C3.gens()
         (t0, t1)
         sage: U3.is_isomorphic(C3)
-        #I  Forcing finiteness test
         True
         sage: U3.as_classical_group()
         Subgroup generated by [(1,7,6)(3,19,14)(4,15,10)(5,11,18)(12,16,20),
@@ -1604,7 +1603,6 @@ def as_permutation_group(self, use_classical=True):
             sage: C3 = CubicBraidGroup(3)
             sage: PC3 = C3.as_permutation_group()
             sage: assert C3.is_isomorphic(PC3)  # random (with respect to the occurrence of the info message)
-            #I  Forcing finiteness test
             sage: PC3.degree()
             8
             sage: c = C3([2,1-2])
diff --git a/src/sage/groups/finitely_presented.py b/src/sage/groups/finitely_presented.py
index 9b5f7e422d6..b65566ebeb4 100644
--- a/src/sage/groups/finitely_presented.py
+++ b/src/sage/groups/finitely_presented.py
@@ -1080,7 +1080,6 @@ def direct_product(self, H, reduced=False, new_names=True):
             sage: C7 = G / [G.0**7]; C6 =  G / [G.0**6]
             sage: C14 = G / [G.0**14]; C3 =  G / [G.0**3]
             sage: C7.direct_product(C6).is_isomorphic(C14.direct_product(C3))
-            #I  Forcing finiteness test
             True
             sage: F = FreeGroup(2); D = F / [F([1,1,1,1,1]),F([2,2]),F([1,2])**2]
             sage: D.direct_product(D).as_permutation_group().is_isomorphic(
@@ -1174,7 +1173,6 @@ def semidirect_product(self, H, hom, check=True, reduced=False):
             sage: alpha = (Q.gens(), [a,b])
             sage: S2 = C2.semidirect_product(Q, ([C2.0],[alpha]))
             sage: S1.is_isomorphic(S2)
-            #I  Forcing finiteness test
             True
 
         Dihedral groups can be constructed as semidirect products
@@ -1233,8 +1231,6 @@ def semidirect_product(self, H, hom, check=True, reduced=False):
             sage: Se2 =  D.semidirect_product(C ,id2)
             sage: Dp1 = C.direct_product(D)
             sage: Dp1.is_isomorphic(Se1), Dp1.is_isomorphic(Se2)
-            #I  Forcing finiteness test
-            #I  Forcing finiteness test
             (True, True)
 
         Most checks for validity of input are left to GAP to handle::
diff --git a/src/sage/groups/finitely_presented_named.py b/src/sage/groups/finitely_presented_named.py
index 940d761ef49..20d847be0dd 100644
--- a/src/sage/groups/finitely_presented_named.py
+++ b/src/sage/groups/finitely_presented_named.py
@@ -451,7 +451,6 @@ def QuaternionPresentation():
         sage: Q.order(), Q.is_abelian()
         (8, False)
         sage: Q.is_isomorphic(groups.presentation.DiCyclic(2))
-        #I  Forcing finiteness test
         True
     """
     F = FreeGroup(['a','b'])
@@ -554,12 +553,6 @@ def BinaryDihedralPresentation(n):
         ....:     P = groups.presentation.BinaryDihedral(n)
         ....:     M = groups.matrix.BinaryDihedral(n)
         ....:     assert P.is_isomorphic(M)
-        #I  Forcing finiteness test
-        #I  Forcing finiteness test
-        #I  Forcing finiteness test
-        #I  Forcing finiteness test
-        #I  Forcing finiteness test
-        #I  Forcing finiteness test
     """
     F = FreeGroup('x,y,z')
     x,y,z = F.gens()
diff --git a/src/sage/groups/libgap_mixin.py b/src/sage/groups/libgap_mixin.py
index 3491c9f9db0..b14b050bd3b 100644
--- a/src/sage/groups/libgap_mixin.py
+++ b/src/sage/groups/libgap_mixin.py
@@ -946,4 +946,16 @@ def is_isomorphic(self, H):
             sage: F == G, G == H, F == H
             (False, False, False)
         """
-        return self.gap().IsomorphismGroups(H.gap()) != libgap.fail
+        # If GAP doesn't know that the groups are finite, it will
+        # check. This emits an informational warning, and then
+        # annotates the groups as being finite (assuming they were) so
+        # that future isomorphism checks are silent. This can lead to
+        # apparent non-determinism in the output as statements are
+        # rearranged. There's nothing the user can do about this
+        # anyway, and it happens in trivial cases like the alternating
+        # group on one element, so we prefer to hide the warning.
+        old_warnlevel = libgap.InfoLevel(libgap.InfoWarning)
+        libgap.SetInfoLevel(libgap.InfoWarning, 0)
+        result = self.gap().IsomorphismGroups(H.gap()) != libgap.fail
+        libgap.SetInfoLevel(libgap.InfoWarning, old_warnlevel)
+        return result
diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
index 0729c5a98ad..d9a7321ade4 100755
--- a/src/sage/schemes/curves/projective_curve.py
+++ b/src/sage/schemes/curves/projective_curve.py
@@ -1805,7 +1805,6 @@ def fundamental_group(self):
             ....:             + (x-18*z)*(z^2+11*x*z-x^2)^2)
             sage: G0 = C.fundamental_group()                    # needs sirocco
             sage: G.is_isomorphic(G0)                           # needs sirocco
-            #I  Forcing finiteness test
             True
             sage: C = P.curve(z)
             sage: C.fundamental_group()                         # needs sirocco