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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On $ \mathfrak{F}$-normalizers


Author: Ti Yen
Journal: Proc. Amer. Math. Soc. 26 (1970), 49-56
MSC: Primary 20.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0262366-6
MathSciNet review: 0262366
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Abstract: The concept of system normalizers of a finite solvable group is generalized to any saturated formation $ \mathfrak{F}$. Given a Sylow system $ \Sigma $ of the finite solvable group $ G$ and an $ \mathfrak{F}$-projector $ V$ of $ G$ reducing $ \Sigma $, a sequence $ \{ {H_i}\} $ of subgroups $ {H_i}$, is constructed such that

(i) each $ {H_i}$ reduces $ \Sigma $, and

(ii) the $ \mathfrak{F}$-normalizers of $ \Sigma \cap {H_i}$ in $ {H_i}$ converge to $ V$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0262366-6
Keywords: Solvable group, formation, system normalizer, $ \mathfrak{F}$-normalizer
Article copyright: © Copyright 1970 American Mathematical Society