Abstract
The main aim of this survey paper is to present two orbit theorems and to show how to apply them to obtain a result that can be regarded as a significant step towards the solution of Gluck’s conjecture on large character degrees of finite soluble groups. We also show how to apply them to solve questions about intersections of some conjugacy families of subgroups of finite soluble groups.
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Acknowledgements
This research has been supported by the grant PROMETEO/2017/057 from the Generalitat, Valencian Community, Spain, and by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovación y Universidades and the Agencia Estatal de Investigación, Spain, and FEDER, European Union. The third author is supported by the predoctoral grant 201606890006 from the China Scholarship Council.
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Ballester-Bolinches, A., Esteban-Romero, R., Meng, H. (2020). On Large Orbits of Actions of Finite Soluble Groups: Applications. In: Ortegón Gallego, F., García García, J. (eds) Recent Advances in Pure and Applied Mathematics. RSME Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-41321-7_8
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