Let σ={σ i| i∈ I} be some partition of the set P of all primes, that is, P=∪ i∈ I σ i and σ i∩ σ
j=∅ for all i≠ j. Let G be a finite group. We say that G is: σ-primary if G is a σ i-group for some …

Let σ={σ i| i∈ I} be some partition of the set of all primes P and G a finite group. G is said to
be σ-soluble if every chief factor H/K of G is a σ i-group for some i= i (H/K). A set H of …

Throughout this paper, all groups are finite and σ is some partition of the set of all primes P
(that is,={i| i 2 I}, where P=[i2Ii and i\j=; for all i 6= j). A subgroup A of a group G is said to be …

Throughout this paper, all groups are finite and G always denotes a finite group. Let σ={σ i|
i∈ I} be a partition of the set of all primes P. The group G is said to be: σ-primary if G is a σ i …

В настоящей статье G всегда обозначает группу. Если K и H–подгруппы группы G, где K–
нормальная подгруппа группы H, то фактор-группа группы H по K называется секцией …

Let $ G $ be a finite group, $\sigma=\{\sigma_ {i}| i\in I\} $ some partition of the set $\Bbb {P}
$ of all primes and $\Pi $ a subset of the set $\sigma $. A set ${\cal H} $ of subgroups of $ G …

Let H and B be subgroups of a finite group G such that G= NG (H) B. Then we say that H is
quasipermutable (respectively, S-quasipermutable) in G provided H permutes with B and …

Throughout this paper, all groups are finite and G always denotes a finite group. Moreover, P
is the set of all primes, P π⊆ and′ π= π. P\If n is an integer, then the symbol () n π denotes …

Let σ={σ i∣ i∈ I} be some partition of the set of all primes and 𝐺 a finite group. Then 𝐺 is
said to be 𝜎-full if 𝐺 has a Hall σ i-subgroup for all i∈ I and 𝜎-primary if 𝐺 is a σ i-group for …

A group G is called a Hall𝒳-group if G possesses a nilpotent normal subgroup N such that
G/N′ is an 𝒳-group. A group G is called an 𝒳o-group if G/Φ (G) is an 𝒳-group. The aim of …