Is it possible that an element of a sylow basis of a finite solvable group G lies in the frattini subgroup of G?(i.e could an element of a sylow basis of a finite solvable group G be a nongenerator subgroup?)
You should tell the reader what a Sylow basis is. Assuming that it s a set of pairwise permutable Sylow subgroups of $G,$ one for each prime divisor, the answer is no. For if $P_{1}$ is a Sylow $p_{1}$subgroup of $G$ belonging to a basis, then deleting $P_{1}$from the generating set given by the Sylow basis leaves a set which generates a Hall $p_{1}^{\prime}$subgroup of $G$ in particular, a proper subgroup of $G.$ 

