Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders. We prove that the fact of imposing specific properties on the second maximal A-invariant subgroups of G determines that G is either soluble or isomorphic to a few non-soluble groups such as PSL(2, 5) or SL(2, 5).
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Funding
National Nature Science Fund of China(12071181)
Nature Science Fund of Shandong Province(ZR2019MA044)
Ministerio de Ciencia Tecnología y Telecomunicaciones (CR)(PGC2018-096872-B-100)
Universitat Jaume I(UJI-B2019-03)
Generalitat Valenciana(Proyecto AICO/2020/298)
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