On Fixed-Point-Free Automorphisms

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• Glen Collins, University of Birmingham
• Thursday 08 May 2014, 16:00-17:00
• Watson Building, Lecture Room A.

If you have a question about this talk, please contact David Craven.

If a finite group A acts on a finite group G in such a way that C_G(A)=1, then one can often say something about the structure of G given properties of A. This idea has long been a source of strong and useful results within finite group theory. I will begin with a brief historical overview of results of this kind before talking in more detail about Khukhro’s recent work in this area, and how a question which I have considered is related to his work. Namely, if we have a group RF where R is cyclic of prime order and F is nilpotent with F=[F,R], which acts on a group G such that C_G(F)=1, then is F(C_G(R)) ≤ F(G)? I will finish by outlining directions for further work and potential obstacles that one might encounter in pursuing these.

This talk is part of the Algebra seminar series.

This talk is included in these lists:

• Algebra seminar
• School of Mathematics events
• Watson Building, Lecture Room A

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