Periodic Groups Saturated with Finite Frobenius Groups with Complements of Orders Divisible by a Prime Number

A finite Frobenius group in which the order of complements is divisible by a prime number p is called a Phi(p)-group. We prove the theorem stating the following. Let G be aperiodic group with a finite elementaof prime order p > 2 saturated with Phi(p)-groups. Then G = F lambda H is a Frobenius group with kernel F and complement H. If G contains an involution i commuting with the element a, then H = C-G (i) and F is Abelian, and H = N-G(a) otherwise.