Infinite Frobenius Groups Generated by Elements of Order 3

A semidirect product [Formula: see text] of groups F and H is called a Frobenius group if the following two conditions are satisfied: (F1) H acts freely on F, that is, [Formula: see text] for f in F and h in H only if h = 1 or f = 1. (F2) Every non-identity element [Formula: see text] of finite order n induces in F by conjugation in G a splitting automorphism, that is, [Formula: see text] for every [Formula: see text]; in other words, the order of [Formula: see text] is equal to n. We describe the normal structure of a Frobenius group with periodic subgroup H generated by elements of order 3.