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Article
On One Open Question of the Theory of \(\sigma \) -Properties of a Finite Group
Let \(\sigma =\{\sigma _{i} \mid i\in I\}\) σ = { ...
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Article
Finite groups in which modularity is a transitive relation
Let G be a group. Then a subgroup A of G is said to be modular in G if (i) \(\langle X, A \cap Z \rangle =\langle X, A \rangle \cap Z\) ...
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Article
A generalization of some results of the theory of permutable subgroups
Let A be a subgroup of a finite group G and \( \mathcal{X} = \{X_ {1}, \ldots , X_ {t} \}\) X ...
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Article
A Generalization of \(\sigma \) -Permutability
Throughout this paper, all groups are finite and G always denotes a finite group; \(\sigma \) σ ...
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Article
A Generalization of Subnormality
Let G be a finite group and \({\mathfrak {F}}\) F a class of groups. A subg...
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Article
On the Lattice of all \({{\mathcal {H}}}\)-Permutable Subgroups of a Finite Group
Let G be a finite group and \(\sigma =\{\sigma _{i} | i\in I\}\)σ={σi|i∈I} is a partition of all primes \(\mathbb {P}\)P. A set \({{{\mathcal {H}}}}\)H of subgroups of G is called a complete Hall \(\sigma \)σ-set...
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Article
Characterizations of Finite \(\sigma \) -Nilpotent and \(\sigma \) -Quasinilpotent Groups
Let \(\sigma =\{\sigma _{i} | i\in I\}\) σ ...
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Article
Finite groups whose n-maximal subgroups are σ-subnormal
Let σ = {σi | i ∈ I} be some partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hallσ-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G, for some i ∈ I, and H cont...
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Article
On σ-semipermutable Subgroups of Finite Groups
Let σ = {σi|i ∈ I} be some partition of the set of all primes ℙ, G a finite group and σ(G) = {σi|σi ∩ π(G) ≠ ∅}. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of H is a H...
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Article
On \(\Pi \) -quasinormal subgroups of finite groups
Let \(\sigma =\{\sigma _{i} | i\in I\}\) σ ...
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Article
On finite groups for which the lattice of S-permutable subgroups is distributive
A subgroup A of a finite group G is said to permute with a subgroup B if \(AB=BA\) ...
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Article
Finite Groups with \({{{\mathcal {H}}}}\) -Permutable Subgroups
Let \(\sigma =\{\sigma _{i}\ |\ i\in I\}\) σ ...
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Article
On Some Results in the Theory of Finite Partially Soluble Groups
This article provides an overview of some recent results and ideas related to the study of finite groups depending on the restrictions on some systems of their sections. In particular, we discuss some properti...
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Article
A generalized CAP-subgroup of a finite group
Let A be a subgroup of a finite group G. We say that A is a generalized CAP-subgroup of G if for each chief factor H/K of G either A avoids H/K or the following holds: (1) If H/K is non-abelian, then |H: (A∩H)K| ...
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Article
On \(S\) -propermutable Subgroups of Finite Groups
Let \(H\) H be ...
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On Boundary Factors and Traces of Subgroups of Finite Groups
A subgroup \(E\) E ...
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On subgroups of hypercentral type of finite groups
The main purpose of this paper is to analyze the influence on the structure of a finite group of some subgroups lying in the hypercenter. More precisely, we prove the following: Let ...
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Article
On Hall subgroups of a finite group
New criteria of existence and conjugacy of Hall subgroups of finite groups are given.
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Article
On G-covering subgroup systems of finite groups
Let \(\mathcal{F}\) be a class of groups and G a finite group. We call a set Σ of subgroups of G a G-cover...
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Article
Finite groups with systems of Σ-embedded subgroups
In recent years, a series of papers about cover-avoiding property of subgroups appeared and all the studies were connected with chief factors of a finite group. However, about the cover-avoiding property of su...
