First-order finite-dimensional equations of the generalized Bhabha type in a space with n spacelike and one timelike dimensions are considered. It is observed that invariance under the connected part SO+(n, 1) of the pseudo-orthogonal group in this space requires the use of a wavefunction transforming according to a representation of the larger group SO+(n + 1, 1). It is shown that though the wavefunction [and each part of it obtained by reduction with respect to SO+(n, 1)] transforms into itself under the strong reflection R also, nevertheless the wave equation in an odd-dimensional space (n + 1 = 2k + 1) may or may not be invariant under R, when the wavefunction employed transforms irreducibly under the connected group SO+(n + 1, 1). Thus, contrary to the suggestion contained in the recent literature, where specific equations are considered, the mere fact of oddness of the dimension of the space does not force the use of representations reducible with respect to the latter group (the matter is representation dependent). It is shown, however, that, irrespective of the representation used and of the dimension of the space, the equation is invariant under a transformation Θ, defined as a combination of an improper transformation which reverses the sign of time and another improper transformation of reflection in any hyperplane in the spacelike variables. It is suggested that TCP in an arbitrary space be identified with Θ rather than with R, which simply reverses the sign of all coordinates.