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This article is cited in 2 scientific papers (total in 2 papers)
On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order
E. I. Khukhroab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b University of Lincoln, Lincoln, UK
Abstract:
It is proved that if a finite $p$-soluble group $G$ admits an automorphism $\varphi$ of order $p^n$ having at most $m$ fixed points on every $\varphi$-invariant elementary abelian $p'$-section of $G$, then the $p$-length of $G$ is bounded above in terms of $p^n$ and $m$; if in addition $G$ is soluble, then the Fitting height of $G$ is bounded above in terms of $p^n$ and $m$. It is also proved that if a finite soluble group $G$ admits an automorphism $\psi$ of order $p^aq^b$ for some primes $p$ and $q$, then the Fitting height of $G$ is bounded above in terms of $|\psi|$ and $|C_G(\psi)|$.
Keywords:
finite soluble group, automorphism, $p$-length, Fitting height.
Received: 08.01.2015
Citation:
E. I. Khukhro, “On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order”, Sibirsk. Mat. Zh., 56:3 (2015), 682–692; Siberian Math. J., 56:3 (2015), 541–548
Linking options:
https://www.mathnet.ru/eng/smj2669 https://www.mathnet.ru/eng/smj/v56/i3/p682
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