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 ...

Let G be a finite group in which every Sylow subgroup is seminormal or abnormal. We prove that G has a Sylow tower. We establish that if a group has a maximal subgroup with Sylow subgroups under the same conditions, then ...

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 ...

A subgroup H of a finite group G is called wide if each prime divisor of the order of G divides the order of H. We obtain a description of finite solvable groups without wide subgroups. It is shown that a finite solvable ...

We investigate the structure of finite soluble groups all whose proper normal subgroups belong to some class of groups, namely a Fitting class and the class of all supersoluble groups.

Для произвольной насыщенной наследственной формации F, содержащей все нильпотентные группы, получено описание конечных разрешимых групп, в которых каждая примарная подгруппа самонормализуема или F-субнормальна.