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 ...

It is proved that if π-Hall subgroup is a supersolvable group then the derived π-length of a π-solvable group G is at most 1 + maxr∈π lra(G), where lra(G) is the derived r-length of a π-solvable group G.

We investigate groups in which maximal subgroups of even order are primary or biprimary. We also research soluble groups with restriction on a number of prime devisors of some proper subgroup orders. We give applications ...

We investigate a finite group G with F-subnormal Sylow subgroups, where F is a subgroup-closed formation and A1A⊆F⊆NA. We prove that G is soluble and the derived subgroup of each metanilpotent subgroup is nilpotent. We ...

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 ...

Let H be a non-normal maximal subgroup of a finite solvable group G, and let q ∈ π(F (H/CoreGH)). It is proved that G has a Sylow q-subgroup Q such that NG(Q) ⊆ H.

Environmental protection of territories of landfills includes filtrates treatment, that occur in the body of a landfill and are extremely toxic, as they have harmful effect on flora, fauna and people and thatʼs why ...

W artykule określone są cechy polityki regionalnej, ocharakteryzowane podstawowe modele wzrostu gospodarczego i strategie rozwoju regionalnego, systematyzowane doświadczenia związane z rozwojem regionalnym Unii Europejskiej ...