%0 Journal Article %T On functional bases of the first-order differential invariants for non-conjugate subgroups of the Poincar¨¦ group $P(1,4)$ %A V.M. Fedorchuk %A V.I. Fedorchuk %J Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica %D 2008 %I Krak¨®w : Wydawnictwo Naukowe Uniwersytetu Pedagogicznego %X It is established which functional bases of the first-order differential invariants of the splitting and non-splitting subgroups of the Poincar¨¦ group $P(1,4)$ are invariant under the subgroups of the extended Galilei group $widetilde G(1,3) subset P(1,4)$. The obtained sets of functional bases are classified according to dimensions. %U http://studmath.up.krakow.pl/index.php/studmath/article/view/75