  Fractional supersymmetry denotes a generalisation of supersymmetry which may
be constructed using a single real generalised Grassmann variable, $\theta =
\bar{\theta}, \, \theta^n = 0$, for arbitrary integer $n = 2, 3, ...$. An
explicit formula is given in the case of general $n$ for the transformations
that leave the theory invariant, and it is shown that these transformations
possess interesting group properties. It is shown also that the two generalised
derivatives that enter the theory have a geometric interpretation as generators
of left and right transformations of the fractional supersymmetry group.
Careful attention is paid to some technically important issues, including
differentiation, that arise as a result of the peculiar nature of quantities
such as $\theta$.
