In this paper we consider finite groups G such that every non-cyclic maximal subgroup in its Sylow subgroups is subnormal in G. In particular, we prove that such solvable groups have an ordered Sylow tower.

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 with seminormal supersoluble subgroups ...

A subgroup A of a group G is called seminormal in G, if there exists a subgroup B such that G = AB and AX is a subgroup of G for every subgroup X of B. We introduce the new concept that unites subnormality and seminormality. A ...

In this paper, we study solvable groups in which rn(F) is at most 2. In particular, we investigated groups of odd order and A4-free groups with this property. Exact estimations of the derived length and nilpotent length ...

We consider the structure of a finite group having a normal series whose factors have bicyclic Sylow subgroups. In particular, we investigate groups of odd order and A4-free groups with this property. Exact estimations ...

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, not necessarily distinct. It is established ...