CHARACTERIZATION OF MODULAR FROBENIUS GROUPS OF SPECIAL TYPE

In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G＇ as a modular Frobenius kernel has no more than four conjugacy classes in G.

Infinite Frobenius Groups Generated by Elements of Order 3

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.

The Jacobson and Brown-McCoy Radicals of Certain Group Rings

In this paper, we determine the Jacobson radicals and Brown-McCoy radicals of group rings of certain non-abelian groups and generalize some known results.

The Class Number of Derived Subgroups and the Structure of Camina Groups

A finite group G is called a Camina group if G has a proper normal subgroup N such that gN is precisely a conjugacy class of G for any g ∈E G - N. In this paper, the structure of a Camina group G is determined when N is a union of 2, 3 or 4 conjugacy classes of G.

Finite Groups whose Abelian Subgroup Orders Are Consecutive Integers

In this paper we give a complete classification of finite groups whose proper abelian subgroup orders are consecutive integers.

On Coprime G-conjugacy Class Sizes in a Normal Subgroup

Let N be a normal subgroup of a group G. Suppose that the positive integers m 〉 n are two longest non-central G-conjugacy class sizes of N with （m, n） = 1. The purpose of this paper is to determine the structure of N and give the N-conjugacy class sizes of the elements in N under that assumption that m is square free.

Finite Groups in Which Every Subgroup Is Abelian or Normal

The main object of this paper is to investigate the finite groups in which every subgroup is either abelian or normal. We obtain a characterization of the groups for the nonnilpotent case, and we also give some properties for the nilpotent case.

A Noteof CP_(2) Groups

A new class CP_(2) groups of finite groups was characterized by using an inequality of the orders of elements.In this short paper we give a note of CP_(2) groups since CP_(2) groups is a subclass of CP(EPPO)groups.Moreover,we discuss the struc-ture of finite p groups contained in CP 2 groups.

Typical Frobenius Coverings

A covering p from a Cayley graph Cay（G, X） onto another Cay（H, Y） is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p ： G →H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay（H, Y）. We show that any typical Frobenius covering Cay（G, X） of Cay（H, Y） can be derived from an epimorphism /from G to H which is determined by an automorphism f of H. If Cay（G, X1） and Cay（G, X2） are two isomorphic typical Frobenius coverings under a graph isomorphism Ф, some properties satisfied by Фare given.