Polynomials with frobenius galois groups

An effective characterization of polynomials of degree n whose Galois groups are Frobenius groups with kernel of order n is given. Some examples of such polynomials are listed.     

Transversal designs associated with frobenius groups

To any Frobenius group G (of degree s, with Frobenius complement of order k) we associate an (s,k) -transversal design (G) which admits G as a point-regular collineation group. (G) is in fact also a dual translation net and furthermore admits a flag-regular collineation group. Also, (G) has two orthogonal resolutions. Conversely, we will characterize the Frobenius groups among the point-regular collineation groups of resolvable transversal designs. We also exhibit two further classes of flag-regular transversal designs. Finally, we completely determine the possible parameters of TD's constructed as above.Dedicated to Professor R. Artzy on the occasion of his 70th birthday     

Solvability of finite groups with 10 p elements of maximal order

It is proved that finite groups with 10_p elements of the largest order, wherep ≥ 23 a prime, are solvable in this article. Consequently it follows that all finite group with 10p elements of largest order are solvable by some other results.     

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.     

On finite groups with prime-power order S-quasinormally embedded subgroups

A subgroup H of a finite group G is said to be S-quasinormally embedded in G if for each prime p dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G. In this paper we investigate the structure of finite groups that have some S-quasinormally embedded subgroups of prime-power order, and new criteria for p-nilpotency are obtained.     

Characterization of the finite simple groups by spectrum and order

We give an affirmative answer to Question 12.39 in the Kourovka Notebook. Namely, it is proved that a finite simple group and a finite group having equal orders and same sets of element orders are isomorphic.