A. Martínez-Pastor

Fitting classes and products of totally permutable groups

The second and third authors have been supported by Proyecto PB 97-0674-C02-02 of DGESIC, Ministerio de Educacion y Cultura, Spain.

Injectors and Radicals in Products of Totally Permutable Groups

Abstract Two subgroups H and K of a group G are said to be totally permutable if every subgroup of H permutes with every subgroup of K. In this paper the behaviour of radicals and injectors associated to Fitting classes in a product of pairwise totally permutable finite groups is studied.

On Sylow normalizers of finite groups

The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent Hall subgroups for given sets of primes are exactly the subgroup-closed saturated formations satisfying the following property: a group belongs to the class if and only if its Sylow normalizers do so. The paper analyzes the extension of this research to the universe of all finite groups.

Square-free class sizes in products of groups

Abstract We obtain some structural properties of a factorised group G = A B , given that the conjugacy class sizes of certain elements in A ∪ B are not divisible by p 2 , for some prime p. The case when G = A B is a mutually permutable product is especially considered.

Prime Power Indices in Factorised Groups

Let the group

Zeros of irreducible characters in factorised groups

G=AB

On finite products of groups and supersolubility

G=AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in