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A coprime action version of a solubility criterion of Deskins

  • Antonio BeltránEmail author
  • Changguo Shao
Article
  • 28 Downloads

Abstract

Let A and G be finite groups of relatively prime orders and suppose that A acts on G via automorphisms. We demonstrate that if G has a maximal A-invariant subgroup M that is nilpotent and the Sylow 2-subgroup of M has class at most 2, then G is soluble. This result extends, in the context of coprime action, a solubility criterion given by W.E. Deskins.

Keywords

Soluble groups Maximal subgroups Coprime action Group action on groups 

Mathematics Subject Classification

20D20 20D15 

Notes

Acknowledgements

The first author is partially supported by the Valencian Government, Proyecto PROMETEOII/2015/011 and also by Universitat Jaume I, Grant P11B-2015-77. The second author is supported by the NNSF of China (No. 11301218) and the Nature Science Fund of Shandong Province (No. ZR2014AM020).

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Jaume ICastellónSpain
  2. 2.School of Mathematical SciencesUniversity of JinanShandongChina

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