Cyclic intersections and control of fusion


Isaacs I. M. , KIZMAZ M. Y.

ARCHIV DER MATHEMATIK, vol.113, no.6, pp.561-563, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 113 Issue: 6
  • Publication Date: 2019
  • Doi Number: 10.1007/s00013-019-01359-w
  • Journal Name: ARCHIV DER MATHEMATIK
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.561-563
  • Keywords: Fusion, Transfer, Strongly embedded
  • Middle East Technical University Affiliated: No

Abstract

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.