Abstract
AbstractLet G be a finite group and assume that a finite group of automorphisms A acts on G, such that the orders of A and G are relatively prime. We prove that the fact of imposing certain conditions on the set of maximal A-invariant subgroups of G, relating to nilpotency, p-nilpotency, normality or having p’-order, determines properties on the structure of G such as solubility, p-solubility or p-nilpotency.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
Reference12 articles.
1. Beltrán, A., Shao, C.G.: Restrictions on maximal invariant subgroups implying solubility of finite groups. Ann. Mat. Pura Appl. (4) 198, 357–366 (2019). https://doi.org/10.1007/s10231-018-0777-1
2. Beltrán, A., Shao, C.G.: A coprime action version of a solubility criterion of Deskins. Monatsh. Math. (3) 188, 461–466 (2019). https://doi.org/10.1007/s00605-018-1256-x
3. Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of Finite Groups. Oxford University Press, London (1985)
4. Huppert, B.: Endliche Gruppen I. Springer, Berlin (1967)
5. Kizmaz, M.Y.: On the influence of the fixed points of an automorphism to the structure of a group. J. Algebra 572, 326–336 (2021). https://doi.org/10.1016/j.jalgebra.2020.12.025
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