On the structure of the noninvariant factor in some Frobenius groups
type: Item
instance of: scholarly article
title: On the structure of the noninvariant factor in some Frobenius groups
zbMATH Open document ID: 0851.20039
DOI: 10.1007/BF02106623
author: Yanyan Li
published in: Siberian Mathematical Journal
publication date: 1996-11-24T00:00:00Z
review text: The well-known Frobenius theorem was transferred to the classes of periodic (weakly conjugately) biprimitively finite groups. In Theorems 2 and 3 and Corollaries 1 and 2 of the present article we determine the structure of the noninvariant factor in such Frobenius groups, thus giving a partial answer to problem 6.53 of the Kourovka Notebook [1986; Zbl 0625.20001]. In Theorem 1 we characterize weakly conjugately biprimitively finite groups of regular automorphisms of abelian groups, which implies in particular a positive solution of problem 10.60 of [loc. cit.] for the indicated class of groups. In the article we construct an example of a periodic weakly conjugately biprimitively finite but not locally finite Frobenius group, solving so problem 6.54 of [loc. cit.].
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 917100
zbMATH Keywords: Frobenius theorem
zbMATH Keywords: biprimitively finite groups
zbMATH Keywords: Frobenius groups
zbMATH Keywords: weakly conjugately biprimitively finite groups
zbMATH Keywords: regular automorphisms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 917100