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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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Keywords: Solvable group, formation, system normalizer, <!– MATH $\mathfrak {F}$ –> <IMG WIDTH="18" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$\mathfrak {F}$">-normalizer
Article copyright: © Copyright 1970 American Mathematical Society