On $B$-injectors of symmetric groups $S_{n}$ and alternating groups $A_{n}$: a new approach

Volume 115 / 2009

M. I. AlAli, Bilal Al-Hasanat, I. Sarayreh, M. Kasassbeh, M. Shatnawi, A. Neumann Colloquium Mathematicum 115 (2009), 247-258 MSC: Primary 20G40. DOI: 10.4064/cm115-2-8

Abstract

The aim of this paper is to introduce the notion of $BG$-injectors of finite groups and invoke this notion to determine the $B$-injectors of $S_n$ and $A_n$ and to prove that they are conjugate. This paper provides a new, more straightforward and constructive proof of a result of Bialostocki which determines the $B\hbox {-injector}$s of the symmetric and alternating groups.

Authors

  • M. I. AlAliDepartment of Mathematics
    Mu'tah University
    Alkarak, Jordan
    e-mail
  • Bilal Al-HasanatDepartment of Mathematics
    Mu'tah University
    Alkarak, Jordan
    e-mail
  • I. SarayrehDepartment of Mathematics
    Mu'tah University
    Alkarak, Jordan
  • M. KasassbehDepartment of Mathematics
    Mu'tah University
    Alkarak, Jordan
    e-mail
  • M. ShatnawiDepartment of Mathematics
    Mu'tah University
    Alkarak, Jordan
    e-mail
  • A. NeumannFakultät für Mathematik und Physik
    Universität Tübingen
    Auf der Morgen Stelle
    72076 Tübingen, Germany
    e-mail

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