On finite soluble groups with almost fixed-point-free automorphisms of non-coprime order

2015/01/09 by E. I. Khukhro, Khukhro, E. I. · 1 citation
Mathematics · #20D45 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20D45

paper · pdf · doi:10.48550/arxiv.1501.02071

arxiv created 2015/01/09 · arxiv updated 2015/01/12

Abstract

It is proved that if a finite p-soluble group G admits an automorphism φ of order pⁿ 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 pⁿ and m; if in addition the group G is soluble, then the Fitting height of G is bounded above in terms of pⁿ and m. It is also proved that if a finite soluble group G admits an automorphism ψ of order p^aq^b for some primes p,q, then the Fitting height of G is bounded above in terms of |ψ| and |C_G(ψ)|.

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