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Adolfo Ballester-Bolinches, Hermann Heineken and Francesca Spagnuolo.
On Sylow permutable subgroups of finite groups.
Forum Math., 29(6):1307-1310, 2017.
A subgroup H of a group G is called Sylow permutable, or S-permutable, in G if H permutes with all Sylow p-subgroups of G for all primes p. A group G is said to be a PST-group if Sylow permutability is a transitive relation in G. We show that a group G which is factorised by a normal subgroup and a subnormal PST-subgroup of odd order is supersoluble. As a consequence, the normal closure S^G of a subnormal PST-subgroup S of odd order of a group G is supersoluble, and the subgroup generated by subnormal PST-subgroups of G of odd order is supersoluble as well.
2020 Mathematics Subject Classification: 20D20, 20D35, 20D40, 20E15.
Keywords: Finite groups, subnormal subgroups, permutability, S-permutability.