Evgeny Khukhro’s talk in Brasilia

Algebra in Lincoln

P1010744a talk271115

On 27 November 2015 Evgeny Khukhro gave a talk at Algebra Seminar of University of Brasilia  Finite groups with a Frobenius group of automorphisms whose kernel is generated by a splitting automorphism of prime order.

Abstract: It is proved that if a finite group $latex G$ admits a Frobenius group of automorphisms $latex FH$ with complement $latex H$ whose kernel $latex F=langlevarphirangle$ is generated by a splitting automorphism $latex varphi$ of prime order $latex p$ (that is, such that $latex xx^{varphi}cdots x^{varphi^{p-1}}=1$ for all $latex xin G$), then $latex G$ is nilpotent of class bounded in terms of $latex p$ and the derived length of $latex C_G(H)$.  The proof is based on the author’s original method of elimination of operators by nilpotency and a joint result with P. Shumyatsky about groups of prime exponent corresponding to the case $latex varphi =1$.

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