Infinite Frobenius Groups Generated by Elements of Order 3

• 作者: Nanying Yang Daria Victorovna Lytkina Victor Danilovich Mazurov Archil Khazeshovich Zhurtov
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 741-748
• 页数: 8页
• 语种: 英文
• DOI: 10.1142/S1005386720000619

摘要

A semidirect product G =F λ 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,ffh...fhn-1 =1 for every f ∈ F;in other words,the order of fh-1 is equal to n.We describe the normal structure of a Frobenius group with periodic subgroup H generated by elements of order 3.