diff --git a/NEWS.md b/NEWS.md
index 84ca00e2f7..ecb9a0bfef 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -5,6 +5,12 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [0.9.2] - 2023-10-26
+
+### Added
+
+- `rand(G; vector_at=Identity(G))` now works for translation, special orthogonal and special Euclidean groups `G` (issue [#665](https://github.com/JuliaManifolds/Manifolds.jl/issues/665)).
+
 ## [0.9.1] - 2023-10-25
 
 ### Added
diff --git a/Project.toml b/Project.toml
index 8f2d4c8e94..a0276cde46 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Manifolds"
 uuid = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
 authors = ["Seth Axen <seth.axen@gmail.com>", "Mateusz Baran <mateuszbaran89@gmail.com>", "Ronny Bergmann <manopt@ronnybergmann.net>", "Antoine Levitt <antoine.levitt@gmail.com>"]
-version = "0.9.1"
+version = "0.9.2"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
diff --git a/src/groups/GroupManifold.jl b/src/groups/GroupManifold.jl
index c8983731be..2698bc48e6 100644
--- a/src/groups/GroupManifold.jl
+++ b/src/groups/GroupManifold.jl
@@ -102,7 +102,7 @@ function is_vector(
             return false
         end
     end
-    return is_vector(G.manifold, identity_element(G), X, false, te; kwargs...)
+    return is_vector(G.manifold, identity_element(G), X, false; error=error, kwargs...)
 end
 
 Base.show(io::IO, G::GroupManifold) = print(io, "GroupManifold($(G.manifold), $(G.op))")
diff --git a/src/groups/general_unitary_groups.jl b/src/groups/general_unitary_groups.jl
index 40c56a179d..39faa74d03 100644
--- a/src/groups/general_unitary_groups.jl
+++ b/src/groups/general_unitary_groups.jl
@@ -34,13 +34,16 @@ function allocate_result(
     return allocate(X)
 end
 function allocate_result(
-    ::GeneralUnitaryMultiplicationGroup,
+    M::GeneralUnitaryMultiplicationGroup,
     ::typeof(log),
     ::Identity{MultiplicationOperation},
     q,
 )
     return allocate(q)
 end
+function allocate_result(M::Rotations, ::typeof(rand), ::Identity{MultiplicationOperation})
+    return similar(Matrix{Float64}, representation_size(M)...)
+end
 
 decorated_manifold(G::GeneralUnitaryMultiplicationGroup) = G.manifold
 
diff --git a/src/groups/translation_group.jl b/src/groups/translation_group.jl
index cbc752acab..a52f9a1731 100644
--- a/src/groups/translation_group.jl
+++ b/src/groups/translation_group.jl
@@ -33,6 +33,10 @@ end
     end
 end
 
+function allocate_result(M::Euclidean, ::typeof(rand), ::Identity{AdditionOperation})
+    return similar(Array{Float64}, representation_size(M)...)
+end
+
 exp!(::TranslationGroup, q, ::Identity{AdditionOperation}, X) = copyto!(q, X)
 
 has_biinvariant_metric(::TranslationGroup) = true
diff --git a/test/groups/general_unitary_groups.jl b/test/groups/general_unitary_groups.jl
index a3829e2990..d393c07819 100644
--- a/test/groups/general_unitary_groups.jl
+++ b/test/groups/general_unitary_groups.jl
@@ -74,6 +74,9 @@ include("group_utils.jl")
             0.4070678736115306 0.10586374034761421 -0.43156436122007846 0.0
         ]
         @test volume_density(M, p, X) ≈ 0.710713830700454
+
+        # random Lie algebra element
+        @test is_vector(M, Identity(M), rand(M; vector_at=Identity(M)))
     end
 
     @testset "Unitary Group" begin
diff --git a/test/groups/special_euclidean.jl b/test/groups/special_euclidean.jl
index c4cd336dc0..0030a38b72 100644
--- a/test/groups/special_euclidean.jl
+++ b/test/groups/special_euclidean.jl
@@ -100,6 +100,8 @@ using Manifolds:
             @test w2mat ≈ affine_matrix(G, pts[1]) * screw_matrix(G, X_pts[1])
             @test screw_matrix(G, w2mat) === w2mat
 
+            @test is_vector(G, Identity(G), rand(G; vector_at=Identity(G)))
+
             test_group(
                 G,
                 pts,
diff --git a/test/groups/translation_group.jl b/test/groups/translation_group.jl
index 5c1b43d75c..e88704ff72 100644
--- a/test/groups/translation_group.jl
+++ b/test/groups/translation_group.jl
@@ -1,6 +1,8 @@
 include("../utils.jl")
 include("group_utils.jl")
 
+using Manifolds: LeftForwardAction, RightBackwardAction
+
 @testset "Translation group" begin
     @testset "real" begin
         G = TranslationGroup(2, 3)
@@ -42,6 +44,8 @@ include("group_utils.jl")
                 test_vee_hat_from_identity=true,
             )
         end
+
+        @test is_vector(G, Identity(G), rand(G; vector_at=Identity(G)))
     end
 
     @testset "complex" begin