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The Prefrattini Residual

Name: The Prefrattini Residual
Creator: H. Bechtell
Keywords: 4. Education, 0103 physical sciences, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, 0101 mathematics, 01 natural sciences

The prefrattini residual

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Mar 1976Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 55, page 267 (issn: 0002-9939,

Authors: H. Bechtell;

doi: 10.2307/2041704 , 10.1090/s0002-9939-1976-0409633-6

The Prefrattini Residual

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Abstract

The structure of a prefrattini subgroup in a finite solvable group is related to the structure of the prefrattini residual, that is, the residual for the formation of solvable n C nC -groups. In particular this structure can be identified with the system normalizers of a lower nilpotent series in the prefrattini residual. Moreover, the prefrattini subgroups form a complete conjugate class within this residual and also contain the system normalizers of the residual.

Keywords

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks

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