Timmesfeld's replacement theorem
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This article defines a replacement theorem
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Statement
Suppose is a finite group, is a prime number, and is a faithful -module, i.e., a vector space over the field of equipped with a -action. Consider the set of elementary abelian -subgroups of such that for all subgroups of . Suppose . Then, we have:
- is nontrivial.
- . In particular, .
- .
Related facts
- Thompson's replacement theorem for abelian subgroups
- Glauberman's replacement theorem
- Corollary of Timmesfeld's replacement theorem for elementary abelian subgroups
References
Journal references
- A remark on Thompson's replacement theorem and a consequence by Franz Georg Timmesfeld, Archiv der Mathematik, ISSN 1420-8938 (Online), ISSN 0003-889X (Print), Volume 38,Number 6, Page 491 - 495(Year 1982): This paper proves a result now known as Timmesfeld's replacement theorem. There are two corollaries, the corollary for abelian subgroups and the corollary for elementary abelian subgroups.^{Official copy}^{More info}