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On permutable subgroups of finite groups

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Abstract.

Let \( \frak Z \) be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, \( \frak Z \) contains exactly one and only one Sylow p-subgroup of G. A subgroup H of a finite group G is said to be \( \frak Z \)-permutable if H permutes with every member of \( \frak Z \). The purpose here is to study the influence of \( \frak Z \)-permutability of some subgroups on the structure of finite groups. Some recent results are generalized.

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Received: 14 May 2001

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Asaad, M., Heliel, A. On permutable subgroups of finite groups. Arch.Math. 80, 113–118 (2003). https://doi.org/10.1007/s00013-003-0782-4

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  • DOI: https://doi.org/10.1007/s00013-003-0782-4

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