  `Shape dynamics' is meant here in the sense of a type of conformogeometrical
reformulation of GR, some of which have of late been considered as
generalizations of or alternatives to GR. This note concerns in particular
cases based on the notion of volume-preserving conformal transformations
(VPCTs), in the sense of preserving a solitary global volume of the universe
degree of freedom. The extent to which various ways of modelling VPCTs make use
of group theory at all, in a congruous manner, and with minimal departure from
standard Lie group theory, is considered. This points to changing conception of
VPCTs from the current finite integral implementation to an infinitesimal
differential implementation (or to avoiding using them at all). Some useful
observations from flat-space conformal groups (well-known from CFT) concerning
the existence or otherwise of VPCT groups are also provided.
