On Hall subgroups of a finite group
New criteria of existence and conjugacy of Hall subgroups of finite groups are given.
Minimal formations of universal algebras
A class ℱ of universal algebras is called a formation if the following conditions are satisfied: 1) Any homomorphic image of A ∈ ℱ is in ℱ; 2) If α₁, α₂ are congruences on A and , i = 1,2, then A/(α₁∩α₂) ∈ ℱ. We prove that any formation generated by a simple algebra with permutable congruences is minimal, and hence any formation containing a simple algebra, with permutable congruences, contains a minimum subformation. This result gives a partial answer to an open problem of Shemetkov and Skiba...
On -permutably embedded subgroups of finite groups
Let be some partition of the set of all primes , be a finite group and . A set of subgroups of is said to be a complete Hall -set of if every non-identity member of is a Hall -subgroup of and contains exactly one Hall -subgroup of for every . is said to be -full if possesses a complete Hall -set. A subgroup of is -permutable in if possesses a complete Hall -set such that = for all and all . A subgroup of is -permutably embedded in if is -full...
On a problem of the theory of multiply local formations.
SE-supplemented subgroups of finite groups
On the influence of the indices of normalizers of Sylow subgroups on the structure of a finite -soluble group.
On the Shemetkov problem for Fitting classes.
-semipermutable subgroups of finite groups.
-primitive subgroups of finite groups.
Finite groups in which the normalizers of Sylow 3-subgroups are of odd or primary index.
On nonnilpotent groups in which every two 3-maximal subgroups are permutable.
Finite groups in which Sylow normalizers have nilpotent Hall supplements.
Frattini theory for classes of finite universal algebras of Mal'tsev varieties.
-covering systems of subgroups for classes of -supersoluble and -nilpotent finite groups.
-quasinormal subgroups.
Page 1