diff --git a/.github/workflows/haskell.yml b/.github/workflows/haskell.yml
index 6a52bed..8273cf2 100644
--- a/.github/workflows/haskell.yml
+++ b/.github/workflows/haskell.yml
@@ -19,7 +19,7 @@ jobs:
     name: GHC ${{ matrix.ghc }} on ${{ matrix.os }}
     steps:
     - uses: actions/checkout@v2
-    - uses: actions/setup-haskell@v1
+    - uses: haskell/actions/setup@v1
       with:
         ghc-version: ${{ matrix.ghc }}
     - name: Cache
diff --git a/ChangeLog.md b/ChangeLog.md
index f88176e..c8d1c4d 100644
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,5 +1,11 @@
 # Revision history for groups
 
+## Unreleased
+
+* `Abelian` is now just a small wrapper around `Group` + `Commutative` from
+  `commutative-semigroups`, which was forked out from this library to relax the
+  superclass.
+
 ## 0.5.3 - 2021-05-14
 
 * Fix bug in `generated'`
diff --git a/groups.cabal b/groups.cabal
index df1a273..a36caf5 100644
--- a/groups.cabal
+++ b/groups.cabal
@@ -23,5 +23,6 @@ library
   exposed-modules:     Data.Group
   -- other-modules:
   build-depends:       base >= 4.6 && < 5
+                     , commutative-semigroups >= 0.0 && < 0.1
   hs-source-dirs:      src
   default-language:    Haskell2010
diff --git a/src/Data/Group.hs b/src/Data/Group.hs
index 6aec99e..5a010dd 100644
--- a/src/Data/Group.hs
+++ b/src/Data/Group.hs
@@ -1,11 +1,14 @@
-{-# LANGUAGE CPP           #-}
+{-# LANGUAGE CPP                  #-}
+{-# LANGUAGE FlexibleInstances    #-}
+{-# LANGUAGE UndecidableInstances #-}
 #if MIN_VERSION_base(4,12,0)
-{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE TypeOperators        #-}
 #endif
 
 module Data.Group where
 
 import Data.Monoid
+import Data.Semigroup.Commutative
 import Data.Ord
 import Data.List (unfoldr)
 #if MIN_VERSION_base(4,7,0)
@@ -98,32 +101,9 @@ instance Group a => Group (Down a) where
   invert (Down a) = Down (invert a)
 #endif
 
--- |An 'Abelian' group is a 'Group' that follows the rule:
---
--- @a \<> b == b \<> a@
-class Group g => Abelian g
-
-instance Abelian ()
-
-instance Num a => Abelian (Sum a)
-
-instance Fractional a => Abelian (Product a)
-
-instance Abelian a => Abelian (Dual a)
-
-instance Abelian b => Abelian (a -> b)
-
-instance (Abelian a, Abelian b) => Abelian (a, b)
-
-instance (Abelian a, Abelian b, Abelian c) => Abelian (a, b, c)
-
-instance (Abelian a, Abelian b, Abelian c, Abelian d) => Abelian (a, b, c, d)
-
-instance (Abelian a, Abelian b, Abelian c, Abelian d, Abelian e) => Abelian (a, b, c, d, e)
-
-#if MIN_VERSION_base(4,11,0)
-instance Abelian a => Abelian (Down a)
-#endif
+-- |An 'Abelian' group is a 'Group' that is also 'Commutative'
+class (Group g, Commutative g) => Abelian g
+instance (Group g, Commutative g) => Abelian g
 
 -- | A 'Group' G is 'Cyclic' if there exists an element x of G such that for all y in G, there exists an n, such that
 --
@@ -163,8 +143,6 @@ instance Group (Proxy x) where
   _ ~~ _ = Proxy
   pow _ _ = Proxy
 
-instance Abelian (Proxy x)
-
 instance Cyclic (Proxy x) where
   generator = Proxy
 #endif
@@ -183,10 +161,6 @@ instance Group a => Group (Identity a) where
   invert (Identity a) = Identity (invert a)
   Identity a ~~ Identity b = Identity (a ~~ b)
 
-instance Abelian a => Abelian (Const a x)
-
-instance Abelian a => Abelian (Identity a)
-
 instance Cyclic a => Cyclic (Const a x) where
   generator = Const generator
 
@@ -210,15 +184,9 @@ instance Group (f (g a)) => Group ((f :.: g) a) where
   invert (Comp1 xs) = Comp1 (invert xs)
   Comp1 xs ~~ Comp1 ys = Comp1 (xs ~~ ys)
 
-instance (Abelian (f a), Abelian (g a)) => Abelian ((f :*: g) a)
-
-instance Abelian (f (g a)) => Abelian ((f :.: g) a)
-
 instance Group a => Group (Op a b) where
   invert (Op f) = Op (invert f)
   pow (Op f) n = Op (\e -> pow (f e) n)
-
-instance Abelian a => Abelian (Op a b)
 #endif
 
 #if MIN_VERSION_base(4,11,0)