Abstract
In general, given a finite group G, a prime p and a p-subgroup R of G, the sylowizers of R in G are not conjugate. In this paper we afford some conditions to achieve the conjugation of the sylowizers of R in a p-soluble group G, among others
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1.
p = 2 and the Sylow 2-subgroups of G are dihedral or quaternion.
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2.
The Sylow p-subgroups of G have order at most p 3.
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3.
p is odd, R is abelian and every element of order p in C G (R) lies in R.
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Communicated by F. De Giovanni.
This research has been supported by Grants: MTM2004-06067-C02-01 and MTM 2004-08219-C02-01, MEC (Spain) and FEDER (European Union).
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Iranzo, M.J., Lafuente, J.P. & Pérez-Monasor, F. On sylowizers in finite p-soluble groups. Ricerche mat. 56, 189–194 (2007). https://doi.org/10.1007/s11587-007-0012-7
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DOI: https://doi.org/10.1007/s11587-007-0012-7