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 | References | Similar Articles | Additional Information
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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Additional Information
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