Abstract
It is proved that if a finite p-soluble group G admits an automorphism φ of order p n having at most m fixed points on every φ-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 ψ of order p a q b for some primes p and q, then the Fitting height of G is bounded above in terms of |ψ| and |C G (ψ)|.
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Original Russian Text Copyright © 2015 Khukhro E.I.
The author was supported by the Russian Science Foundation (Grant 14-21-00065).
To Yuriĭ Leonidovich Ershov on the occasion of his 75th birthday.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 3, pp. 682–692, May–June, 2015; DOI: 10.17377/smzh.2015.56.317.
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Khukhro, E.I. On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order. Sib Math J 56, 541–548 (2015). https://doi.org/10.1134/S0037446615030179
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DOI: https://doi.org/10.1134/S0037446615030179