Singlets of fermionic gauge symmetries

We investigate under which conditions singlets of fermionic gauge symmetries are ''square roots of gravity'' can exist. Their existence si non-trivial because there are no fields neutral in gravity. We tabulate several examples of singlets of global and local supersymmetry and k-symmetry and show how in each case the gravity effect if cancelled by other gauge symmetries. We point out that the finding of k-symmetry singlets is essential for a covariant quantization of extended objects with manifest spacetime supersymmetry. Their role in string compactification is discussed. (orig.)