On $\mathfrak {F}$-normalizers and $\mathfrak {F}$-hypercenter
Author:
Nobuo Inagaki
Journal:
Proc. Amer. Math. Soc. 26 (1970), 21-22
MSC:
Primary 20.40
DOI:
https://doi.org/10.1090/S0002-9939-1970-0263921-X
MathSciNet review:
0263921
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Abstract | References | Similar Articles | Additional Information
Abstract: In this note, we shall prove a theorem which is a generalization of the following theorem: Let $G$ be a soluble group, then the intersection of all system normalizers of $G$ is the hypercenter of $G$.
- Roger Carter and Trevor Hawkes, The ${\cal F}$-normalizers of a finite soluble group, J. Algebra 5 (1967), 175β202. MR 206089, DOI https://doi.org/10.1016/0021-8693%2867%2990034-8
- Bertram Huppert, Zur Theorie der Formationen, Arch. Math. (Basel) 19 (1969), 561β574 (1969) (German). MR 244382, DOI https://doi.org/10.1007/BF01899382
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
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Keywords:
Local formation,
Sylow system,
<!β MATH $\mathfrak {F}$ β> <IMG WIDTH="18" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$\mathfrak {F}$">-normalizer,
<!β MATH $\mathfrak {F}$ β> <IMG WIDTH="18" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img4.gif" ALT="$\mathfrak {F}$">-central-<IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img5.gif" ALT="$p$">-chief factor,
<!β MATH $\mathfrak {F}$ β> <IMG WIDTH="18" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\mathfrak {F}$">-hypercenter
Article copyright:
© Copyright 1970
American Mathematical Society