• Thumbnail

      Finite groups with subnormal non-cyclic subgroups 

      Monakhov, Victor; Trofimuk, Alexander (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
    • Thumbnail

      Finite groups with two supersoluble subgroups 

      Monakhov, Victor; Trofimuk, Alexander (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
    • Thumbnail

      On a finite group having a normal series whose factors have bicyclic Sylow subgroups 

      Monakhov, Victor; Trofimuk, Alexander (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
    • Thumbnail

      On the residual of a finite group with semi-subnormal subgroups 

      Trofimuk, Alexander (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
    • Thumbnail

      Solvable groups with restrictions on Sylow subgroups of the Fitting subgroup 

      Trofimuk, Alexander (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
    • Thumbnail

      Supersolubility of a finite group with normally embedded maximal subgroups in Sylow subgroups 

      Monakhov, Victor; Trofimuk, Alexander (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