Evgeny Khukhro’s talk in Brasilia

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 $G$ admits a Frobenius group of automorphisms $FH$ with complement $H$ whose kernel $F=\langle\varphi\rangle$ is generated by a splitting automorphism $\varphi$ of prime order $p$ (that is, such that $xx^{\varphi}\cdots x^{\varphi^{p-1}}=1$ for all $x\in G$ ), then $G$ is nilpotent of class bounded in terms of $p$ and the derived length of $C_G(H)$ . 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 $\varphi =1$ .