Let G be a finite group. In this paper we obtain some sufficient conditions for the
supersolubility of G with two supersoluble non-conjugate subgroups H and K of prime index …

A subgroup A of a group G is called tcc-subgroup in G, if there is a subgroup T of G such that
G= AT and for any X≤ A and for any Y≤ T, there exists an element u∈〈 X, Y〉 such that XY …

A subgroup H of a group G is called µ-supplemented in G if there exists a subgroup K such
that G= HK and H 1 K is a proper subgroup in G for every maximal subgroup H 1 in H. For …

A subgroup A is called seminormal in a group G if there exists a subgroup B such that G= AB
and AX is a subgroup of G for every subgroup X of B. Studying a group of the form G= AB …

Группой Шмидта называют конечную ненильпотентную группу, все собственные
подгруппы которой нильпотентны. Добавлением к подгруппе A в группе G называется …

Let G be a group. A subgroup H is weakly subnormal in G if H=⟨A,B⟩ for some subnormal
subgroup A and seminormal subgroup B in G. Note that B is seminormal in G if there exists a …

A subgroup A of a finite group G is said to be NS-supplemented in G, if there exists a
subgroup B of G such that G= AB and whenever X is a normal subgroup of A and p ∈ π (B) …

A finite nonnilpotent group is called a Schmidt group if all its proper subgroups are nilpotent.
A subgroup A is called S-seminormal (or SS-permutable) in a finite group G if there is a …

Let H be a subgroup of a finite group G. Then we say that H is propermutable in G provided
G has a subgroup B such that G= NG (H) B and H permutes with all subgroups of B. In this …

Throughout this paper, all groups are finite and G always denotes a finite group. Moreover p
is always supposed to be a prime and π is a subset of the set P of all primes;() G π denotes …