On the irreducibility of the Dirichlet polynomial of an alternating group

Recognizing PSL(2, p) in the non-Frattini chief factors of finite groups

“…Proof of Theorem 3. The proof is analogous to that of [18,Theorem 3]. We present here for the sake of completeness of the paper.…”

“…Proof of Theorem 5. If p = 5 then PSL(2, 5) ∼ = Alt(5) and the result follows from [18,Theorem 2]. Assume now that p > 5 and set S := PSL(2, p).…”

“…If p = 5 then n = 5 and PSL(2, 5) ∼ = Alt(5). The result follows from [18,Proposition 28]. If p = 11 then X = PSL(2, 11), n = 11 and (cf.…”

“…From the proof of Theorem 3, one has the following consequence. In order to mimic the method from [18], we prove the following result.…”