Abstract
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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The authors are grateful to the referee for the careful reading of the paper and his/her useful comments that have improved its presentation.
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This work is supported by the National Nature Science Fund of China (No. 12071181) and the first author is also supported by the Nature Science Fund of Shandong Province (No. ZR2019MA044 and ZR2020MA003). The second author is also supported by Proyecto PGC2018-096872-B-100 MCIN/AEI, by Universitat Jaume I, Proyecto UJI-B2019-03 and by Generalitat Valenciana, Proyecto AICO/2020/298.
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Shao, C., Beltrán, A. Second Maximal Invariant Subgroups and Solubility of Finite Groups. Commun. Math. Stat. 12, 45–54 (2024). https://doi.org/10.1007/s40304-021-00279-y
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DOI: https://doi.org/10.1007/s40304-021-00279-y