Просмотр по автору "Trofimuk, Alexander"
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Finite groups with subnormal non-cyclic subgroups
(De Gruyter, 2014)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.2020-09-17 -
Finite groups with two supersoluble subgroups
(de Gruyter, 2019)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 ...2020-11-10 -
On a finite group having a normal series whose factors have bicyclic Sylow subgroups
(Taylor & Francis Group, 2011)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 ...2020-11-10 -
On the residual of a finite group with semi-subnormal subgroups
(2020)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 ...2020-11-10 -
Solvable groups with restrictions on Sylow subgroups of the Fitting subgroup
(World Scientific Publishing Company, 2016)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 ...2020-11-10 -
Supersolubility of a finite group with normally embedded maximal subgroups in Sylow subgroups
(Pleiades Publishing, Ltd.,, 2018)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 ...2020-11-10