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Archiv der Mathematik

, Volume 113, Issue 6, pp 561–563 | Cite as

Cyclic intersections and control of fusion

  • I. M. IsaacsEmail author
  • M. Yasir Kızmaz
Article
  • 139 Downloads

Abstract

Let H be a subgroup of a finite group G, and suppose that H contains a Sylow p-subgroup P of G. Write \(N = \mathbf{N}_{G}(H)\), and assume that the Sylow p-subgroups of \(H \cap H^g\) are cyclic for all elements \(g \in G\) not lying in N. We show that in this situation, N controls G-fusion in P.

Keywords

Fusion Transfer Strongly embedded 

Mathematics Subject Classification

20D20 

Notes

Reference

  1. 1.
    Isaacs, I.M.: Finite Group Theory. American Mathematical Society, Providence (2008)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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