Action of Aut(G) on the set of maximal subgroups of p-groups

Autores: Sun Xiulu, Mohamed Hamdy
Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 8, Nº. 1, 2023, págs. 2451-2458
Idioma: inglés
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Resumen
- In this paper, we mainly study the action of Aut(G) on the set Ω of all maximal subgroups of G, and we use P to denotethe action of Aut(G) on Ω. When G is a finite non-cyclic abelian p-group, P is transitive. When G is minimal non-abelian,there are three cases. If G is quaternion group, P is transitive; if G is a metacyclic group, P is non-transitive; if G is nota metacyclic group, P is transitive.