diff --git a/gtsam/base/concepts.h b/gtsam/base/concepts.h
index 90f897b90..e4fa6eda9 100644
--- a/gtsam/base/concepts.h
+++ b/gtsam/base/concepts.h
@@ -25,6 +25,9 @@ struct Manifold {
   typedef Chart::value_type type;
 };
 
+struct additive_group_tag {};
+struct multiplicative_group_tag {};
+
 } // namespace traits
 
 template<class T>
@@ -77,16 +80,27 @@ class GroupConcept {
     Group pq = compose(p, q);
     Group d = between(p, q);
     bool test = equal(p, q);
+    operator_usage(p, q, traits::group_flavor<Group>::tag);
   }
 
   bool check_invariants(const Group& a, const Group& b) {
     return (equal(compose(a, inverse(a)), identity))
         && (equal(between(a, b), compose(inverse(a), b)))
-        && (equal(compose(a, between(a, b)), b));
+        && (equal(compose(a, between(a, b)), b))
+        && operator_usage(a, b, traits::group_flavor<Group>::tag)
   }
 
  private:
   Group p,q;
+
+  bool operator_usage(const Group& a, const Group& b, traits::multiplicative_group_tag) {
+    return equals(compose(a, b), a*b);
+
+  }
+  bool operator_usage(const Group& a, const Group& b, traits::additive_group_tag) {
+    return equals(compose(a, b), a+b);
+  }
+
 };
 
 } // namespace gtsam