diff --git a/gtsam/base/concepts.h b/gtsam/base/concepts.h
index 39e707a95..3eabdd3ad 100644
--- a/gtsam/base/concepts.h
+++ b/gtsam/base/concepts.h
@@ -149,6 +149,17 @@ check_invariants(const T& a, const T& b, double tol = 1e-9) {
 }
 } // \ namespace group
 
+#define GTSAM_ADDITIVE_GROUP1(T1,A1,GROUP) \
+namespace group { \
+template<T1 A1> GROUP<A1> compose(const GROUP<A1> &g, const GROUP<A1> & h) { return g + h;} \
+template<T1 A1> GROUP<A1> between(const GROUP<A1> &g, const GROUP<A1> & h) { return h - g;} \
+template<T1 A1> GROUP<A1> inverse(const GROUP<A1> &g) { return -g;} \
+namespace traits { \
+template<T1 A1> struct identity<GROUP<A1> > { static const GROUP<A1> value; typedef GROUP<A1> value_type;};\
+template<T1 A1> const GROUP<A1> identity<GROUP<A1> >::value = GROUP<A1>::Identity();\
+template<T1 A1> struct flavor<GROUP<A1> > { typedef additive_tag type;};\
+}}
+
 #define GTSAM_MULTIPLICATIVE_GROUP2(T1,A1,T2,A2,GROUP) \
 namespace group { \
 template<T1 A1, T2 A2> GROUP<A1,A2> compose(const GROUP<A1,A2> &g, const GROUP<A1,A2> & h) { return g * h;} \
diff --git a/gtsam/geometry/Cyclic.h b/gtsam/geometry/Cyclic.h
index 94d302d5b..f97f05dc8 100644
--- a/gtsam/geometry/Cyclic.h
+++ b/gtsam/geometry/Cyclic.h
@@ -20,34 +20,15 @@
 
 namespace gtsam {
 
-/// Additive Group, using CRTP
-template<typename Derived>
-struct AdditiveGroup {
-  static Derived Identity() {
-    return Derived::Identity();
-  }
-  Derived const * derived() const {
-    return static_cast<Derived const*>(this);
-  }
-  Derived operator+(const AdditiveGroup& h) const {
-    return derived()->operator+(*h.derived());
-  }
-  Derived operator-(const AdditiveGroup& h) const {
-    return derived()->operator-(*h.derived());
-  }
-  Derived operator-() const {
-    return derived()->operator-();
-  }
-};
-
 /// Cyclic group of order N
 template<size_t N>
-class Cyclic : public AdditiveGroup<Cyclic<N> > {
+class Cyclic {
   size_t i_; ///< we just use an unsigned int
 public:
   /// Constructor
   Cyclic(size_t i) :
       i_(i) {
+    assert(i<N);
   }
   // Idenity element
   static Cyclic Identity() {
@@ -81,48 +62,15 @@ public:
 
 };
 
+GTSAM_ADDITIVE_GROUP1(size_t,N,Cyclic)
+
 namespace traits {
-/// Define any additive group to be at least a model of the Group concept
-template<typename G>
-struct structure_category<AdditiveGroup<G> > {
+/// Define cyclic group to be a model of the Group concept
+template<size_t N>
+struct structure_category<Cyclic<N> > {
   typedef group_tag type;
 };
 } // \namespace gtsam::traits
 
-namespace group {
-
-template<typename G>
-G compose(const AdditiveGroup<G>&g, const AdditiveGroup<G>& h) {
-  return g + h;
-}
-
-template<typename G>
-G between(const AdditiveGroup<G>&g, const AdditiveGroup<G>& h) {
-  return h - g;
-}
-
-template<typename G>
-G inverse(const AdditiveGroup<G>&g) {
-  return -g;
-}
-
-namespace traits {
-
-/// Define the trait that specifies Cyclic's identity element
-template<typename G> struct identity<AdditiveGroup<G> > {
-  static const G value;
-  typedef G value_type;
-};
-
-template<typename G>
-const G identity<AdditiveGroup<G> >::value = AdditiveGroup<G>::Identity();
-
-/// Define the trait that asserts AdditiveGroup is an additive group
-template<typename G> struct flavor<AdditiveGroup<G> > {
-  typedef additive_tag type;
-};
-
-} // \namespace gtsam::group::traits
-} // \namespace gtsam::group
 } // \namespace gtsam
 
diff --git a/gtsam/geometry/tests/testCyclic.cpp b/gtsam/geometry/tests/testCyclic.cpp
index 95ed1b5b9..dfc94f36e 100644
--- a/gtsam/geometry/tests/testCyclic.cpp
+++ b/gtsam/geometry/tests/testCyclic.cpp
@@ -26,7 +26,7 @@ typedef Cyclic<6> G; // Let's use the cyclic group of order 6
 
 //******************************************************************************
 TEST(Cyclic, Concept) {
-//  BOOST_CONCEPT_ASSERT((IsGroup<G>));
+  BOOST_CONCEPT_ASSERT((IsGroup<G>));
 //  BOOST_CONCEPT_ASSERT((IsGroup<AdditiveGroup<G> >));
   EXPECT_LONGS_EQUAL(0, group::traits::identity<G>::value);
   G g(2), h(3);