diff --git a/CHANGES b/CHANGES
--- a/CHANGES
+++ b/CHANGES
@@ -1,8 +1,17 @@
+* 0.6.2: 20 Dec 2022
+
+- New class and newtypes in `Data.Monoid.Action` (thanks to Manuel Bärenz):
+    - `Torsor` class for transitive group actions
+    - `Regular` and `Conjugate` newtypes for groups acting on themselves
+
 * 0.6.1: 16 Nov 2021
 
 - Add more efficient `stimes` implementations for several `Semigroup`
   instances.  Thanks to BlackCapCoder for the patch!
 - Allow `base-4.16` and test on GHC 9.2.1.
+
+- r1: allow `base-4.16` in benchmarks
+- r2 (15 August 2022): allow `base-4.17` and test with GHC 9.4.
 
 * 0.6: 8 May 2021
 
diff --git a/monoid-extras.cabal b/monoid-extras.cabal
--- a/monoid-extras.cabal
+++ b/monoid-extras.cabal
@@ -1,5 +1,5 @@
 name:                monoid-extras
-version:             0.6.1
+version:             0.6.2
 synopsis:            Various extra monoid-related definitions and utilities
 description:         Various extra monoid-related definitions and utilities,
                      such as monoid actions, monoid coproducts, semi-direct
@@ -14,7 +14,7 @@
 category:            Data
 build-type:          Simple
 cabal-version:       >=1.10
-tested-with:         GHC ==8.4.4 || ==8.6.5 || ==8.8.4 || ==8.10.4 || ==9.0.1 || ==9.2.1
+tested-with:         GHC ==8.4.4 || ==8.6.5 || ==8.8.4 || ==8.10.7 || ==9.0.2 || ==9.2.4 || ==9.4.1
 
 source-repository head
   type: git
@@ -36,7 +36,7 @@
                      Data.Monoid.Split,
                      Data.Monoid.WithSemigroup
 
-  build-depends:     base >= 4.11 && < 4.17,
+  build-depends:     base >= 4.11 && < 4.18,
                      groups < 0.6,
                      semigroupoids >= 4.0 && < 5.4
 
@@ -55,7 +55,7 @@
   hs-source-dirs: benchmarks
   main-is: SemiDirectProduct.hs
   type: exitcode-stdio-1.0
-  build-depends: base          >= 4.3 &&  < 4.16
+  build-depends: base          >= 4.3 &&  < 4.18
                , semigroups
                , criterion
                , monoid-extras
diff --git a/src/Data/Monoid/Action.hs b/src/Data/Monoid/Action.hs
--- a/src/Data/Monoid/Action.hs
+++ b/src/Data/Monoid/Action.hs
@@ -14,9 +14,13 @@
 
 module Data.Monoid.Action
        ( Action(..)
+       , Regular(..)
+       , Conjugate(..)
+       , Torsor(..)
        ) where
 
 import           Data.Semigroup
+import           Data.Group
 
 ------------------------------------------------------------
 --  Monoid and semigroup actions
@@ -81,3 +85,46 @@
 instance Action (Endo a) a where
   act = appEndo
 
+instance Num a => Action Integer (Sum a) where
+  n `act` a = fromInteger n <> a
+
+instance Num a => Action Integer (Product a) where
+  n `act` a = fromInteger n <> a
+
+instance Fractional a => Action Rational (Sum a) where
+  n `act` a = Sum (fromRational n) <> a
+
+instance Fractional a => Action Rational (Product a) where
+  n `act` a = Product (fromRational n) <> a
+
+-- | An action of a group is "free transitive", "regular", or a "torsor"
+--   iff it is invertible.
+--
+--   Given an original value `sOrig`, and a value `sActed` that is the result
+--   of acting on `sOrig` by some `m`,
+--   it is possible to recover this `m`.
+--   This is encoded in the laws:
+--
+--   * @(m `'act'` s) `'difference'` s = m@
+--   * @(sActed `'difference'` sOrig) `'act'` sOrig = sActed@
+class Group m => Torsor m s where
+
+  -- | @'difference' sActed sOrig@ is the element @m@ such that @sActed = m `'act'` sOrig@.
+  difference :: s -> s -> m
+
+-- | Any monoid acts on itself by left multiplication.
+--   This newtype witnesses this action:
+--   @'getRegular' $ 'Regular' m1 `'act'` 'Regular' m2 = m1 '<>' m2@
+newtype Regular m = Regular { getRegular :: m }
+
+instance Semigroup m => Action m (Regular m) where
+  m1 `act` Regular m2 = Regular $ m1 <> m2
+
+instance Group m => Torsor m (Regular m) where
+  Regular m1 `difference` Regular m2 = m1 ~~ m2
+
+-- | Any group acts on itself by conjugation.
+newtype Conjugate m = Conjugate { getConjugate :: m }
+
+instance Group m => Action m (Conjugate m) where
+  m1 `act` Conjugate m2 = Conjugate $ m1 <> m2 ~~ m1