On the structure of the noninvariant factor in some Frobenius groups
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.].
weakly conjugately biprimitively finite groups
scientific article; zbMATH DE number 917100