摘要
A semidirect product G=F⋋H 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,fh=f for f in F and h in H only if^(h)=1 or f=1.(F2)Every non-identity element h∈H of finite order n induces in F by conjugation in G a splitting automorphism,that is,ff^(h)⋯fh^(n−1)=1 for every f∈F;in other words,the order of f^(h−1)is equal to n.We describe the normal structure of a Frobenius group with periodic subgroup H generated by elements of order 3.
基金
The work was supported by the Program of Fundamental Research of the SB RAS no.1.1.1(project no.0314-2019-0001).
