Corollary of Timmesfeld's replacement theorem for abelian subgroups
From Groupprops
This article is about a maximality notion among subgroups, related to abelianness or small class, in a group of prime power order.
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Statement
Suppose is a group of prime power order. Let denote the set of abelian subgroups of maximum order in . If , and is an -invariant abelian subgroup of . Then, is an abelian subgroup of maximum order.
Related facts
- Timmesfeld'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}