Let G be a supersolvable finite group or a solvable one, in which the orders of principal factors are primes or squares of primes; and let exp G divide $n = p_{1}^{a_{1}} p_{2}^{a_{2}} \cdots p_{s}^{a_{s}}$ ($p_{1} > p_{2} > \cdots > p_{s}$ prime numbers). A much simple enunciation is given for essentially known theorems on some systems of laws characterizing G; it is indeed shown that the laws 1.(1) and 1.(2) can be removed from the enunciates of such theorems, getting equivalent systems of laws characterizing G.