Cyclic intersections and control of fusion

Date

2019-12-01

Author

Isaacs, I. M.
Kızmaz, Muhammet Yasir

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Let H be a subgroup of a finite group G, and suppose that H contains a Sylow p-subgroup P of G. Write N=NG(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N = \mathbf{N}_{G}(H)$$\end{document}, and assume that the Sylow p-subgroups of H boolean AND Hg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H \cap H<^>g$$\end{document} are cyclic for all elements g is an element of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g \in G$$\end{document} not lying in N. We show that in this situation, N controls G-fusion in P.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/52111

Journal

ARCHIV DER MATHEMATIK

DOI

https://doi.org/10.1007/s00013-019-01359-w

Collections

Department of Mathematics, Article

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Citation Formats

I. M. Isaacs and M. Y. Kızmaz, “Cyclic intersections and control of fusion,” ARCHIV DER MATHEMATIK, pp. 561–563, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52111.