On the supersolubility of a finite group factorized into pairwise permutable seminormal subgroups

Alexander Trofimuk
2020 Colloquium Mathematicum  
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 study groups G = G1 . . . Gn with pairwise permutable subgroups G1, . . . , Gn such that Gi and Gj are seminormal in GiGj for any i, j ∈ {1, . . . , n}, i = j. In particular, we prove that G is supersoluble in the following cases: G1 is supersoluble and Gi is nilpotent for every i ≥ 2; Gi is supersoluble for any i and G is nilpotent. 2020 Mathematics Subject Classification: 20D10, 20D40.
doi:10.4064/cm8091-12-2019 fatcat:owck7okrpzhcbh6fyhdqnh5t5y