Abstract
This paper, which is one of a series of four, contributes to the proof of the following
Theorem.A finite group admitting a coprime fixed-point-free automorphism α of order rst (r, s andt distinct primes)is soluble.
Here we prove that in a minimal counterexample to the above theorem the set ofα-invariant Sylowp-subgroupsP, such thatC p(α i)≠1 for allα i≠1, generate a soluble subgroup.
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References
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P. J. Rowley,Solubility of finite groups admitting a fixed-point-free automorphism of order rst I, Pac. J. Math.193 (1981), 201–235.
P. J. Rowley,Solubility of finite groups admitting a fixed-point-free automorphism of order rst II, J. Algebra83 (1983), 293–348.
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Rowley, P. Solubility of finite groups admitting a fixed-point-free automorphism of orderrst III. Israel J. Math. 51, 125–150 (1985). https://doi.org/10.1007/BF02772962
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DOI: https://doi.org/10.1007/BF02772962