Infinite Frobenius Groups Generated by Elements of Order 3

作     者：Nanying Yang Daria Vic to rovna Lytkina Victor Danilovich Mazurov Archil Khazeshovich Zhurtov Nanying Yang;Daria Victorovna Lytkina;Victor Danilovich Mazurov;Archil Khazeshovich Zhurtov

作者机构：School of ScienceJiangnan UniversityWuxiJiangsu 214122China Siberian State University of Telecommunications and Information Sciences 630102Kirova 86NovosibirskRussia Sobolev Institute of MathematicsSB RAS630090 Pr.Ak.Koptjug 4NovosibirskRussia Kabardino-Balkarian State Universityul.Chernyshevskogo 173 Nalchik360004Kabardino-BalkariyaRussia 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2020年第27卷第4期

页      面：741-748页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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) 

主　　题：Frobenius group splitting automorphism character table 

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 *** describe the normal structure of a Frobenius group with periodic subgroup H generated by elements of order 3.