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A. Ballester-Bolinches, J. C. Beidleman, H. Heineken, M. C. Pedraza-Aguilera
Prefactorized subgroups in pairwise mutually permutable subgroups
Ann. Math .Pura Appl., 192(6), 1043-1057 (2013)
We continue here our study of pairwise mutually and pairwise totally permutable products. We are looking for subgroups of the product in which the given factorization induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized Carter subgroup and a prefactorized system normalizer exist. A less stringent property have F-residual, F-projector and F-normalizer for any saturated formation F including the supersoluble groups.
MSC: 20D10, 20D20
Keywords: Finite group, Permutability, Factorization, Saturated formation.