Abstract
If G is a finite group and A a Hall p'-subgroup of G, then it is well known that Op(G) is the largest p-subgroup of G, which is normalized by A. In this note, Op(G) is characterized as the largest p-subgroup, whose normalizer contains a Sylow p-subgroup of G and the generalized Fittingsubgroup of A.
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Literatur
Kurzweil, H.: Endliche Gruppen. Springer-Verlag, Berlin, Heidelberg 1977
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Preiser, U. Über den grössten p-Normalteiler einer endlichen Gruppe. Manuscripta Math 37, 65–66 (1982). https://doi.org/10.1007/BF01239946
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DOI: https://doi.org/10.1007/BF01239946