Central elementary extensions of finite \(p\)-groups are studied by cohomological methods, namely, the Hochschild-Serre filtration of the second cohomology group of such an extension. Using this technique, the author reproves a number of results on the Frattini subgroup of finite \(p\)-groups (by Berger-Kovács-Newman, Blackburn, Kahn, Hobby, Thompson and others). Although not necessarily shorter than the original ones, the new proofs provide evidence of how useful cohomological methods can be. There is also constructed an example of a 2-group which contradicts one of the results of \textit{B. Kahn} [in J. Algebra 144, No. 1, 214-247 (1991; Zbl 0777.20019)].