On Theorems of the Sylow Type for Finite Groups

We describe a new class of finite groups for which the D -theorem is true.     

$$G$$ -Covering Subgroup Systems for the Class of All $$\sigma$$ -Nilpotent Finite Groups

Mathematical Notes - Let $$\mathfrak F$$ be a nonempty class of groups and let $$G$$ be a finite group. A set $$\Sigma$$ of subgroups of the group $$G$$ is called a $$G$$ -covering subgroup system...     

On one class of superradical hereditary saturated formations

Under study is some special class of hereditary saturated formations of finite groups. We analyze the role of these formations in the problem of a classification of all superradical formations.     

On the products of ℙ-subnormal subgroups of finite groups

A subgroup H of a finite group G is called ℙ-subnormal in G whenever H either coincides with G or is connected to G by a chain of subgroups of prime indices. If every Sylow subgroup of G is ℙ-subnormal in G then G is called a w-supersoluble group. We obtain some properties of ℙ-subnormal subgroups and the groups that are products of two ℙ-subnormal subgroups, in particular, of ℙ-subnormal w-supersoluble subgroups.     

On finite groups with some subgroups of prime indices

We establish the solvability of each finite group whose every proper nonmaximal subgroup lies in some subgroup of prime index.     

On the existence of solvable normal subgroups in finite groups

The structure of a finite group in dependence on the structure of the subgroups generated by elements of its conjugate class is considered. Translated fromMatematischeskie Zametki, Vol. 61, No. 5, pp. 755–758, May, 1997. Translated by A. I. Shtern     

On the finite groups of supersoluble type

We study the properties of finite groups in which every Sylow subgroup can be connected to the group by a chain of subgroups of prime indices. We establish the solubility of this type of groups. We prove that the class of all finite groups with this property of Sylow subgroups is a saturated hereditary formation. For these groups we find some analogs of the available theorems on the products of normal supersoluble subgroups.     

On the Kegel–Wielandt $$\sigma$$ -Problem

Mathematical Notes - For an arbitrary partition $$\sigma$$ of the set $$\mathbb{P}$$ of all primes, a sufficient condition for the $$\sigma$$ -subnormality of a subgroup in a finite group is given....     

On a Hall Hypothesis

We obtain a new criterion for the solvability of a finite group with a given family of Hall subgroups.     

On the Existence of $ G $ -Permutable Subgroups in Simple Sporadic Groups

Siberian Mathematical Journal - A subgroup $ A $ of a group $ G $ is $ G $ -permutable in  $ G $ if for every subgroup $ B\leq G $ there is $ x\in G $ satisfying $ AB^{x}=B^{x}A $ ....