Onur, Cansu BetinMathematics2024-07-052024-07-05201831300-00981303-614910.3906/mat-1706-422-s2.0-85046763311https://doi.org/10.3906/mat-1706-42https://search.trdizin.gov.tr/tr/yayin/detay/348801/on-strongly-autinertial-groupsOnur, Cansu Betin/0000-0002-3691-1469A subgroup X of G is said to be inert under automorphisms (autinert) if |X : $X^\\alpha$ ∩ X| is finite for allα ∈ Aut(G) and it is called strongly autinert if | < X, $X^\\alpha$ >: X| is finite for all α ∈ Aut(G). A group is calledstrongly autinertial if all subgroups are strongly autinert. In this article, the strongly autinertial groups are studied. Wecharacterize such groups for a finitely generated case. Namely, we prove that a finitely generated group G is stronglyautinertial if and only if one of the following hold:i) G is finite;ii) G = ⟨a⟩ ⋉ F where F is a finite subgroup of G and ⟨a⟩ is a torsion-free subgroup of G.Moreover, in the preliminary part, we give basic results on strongly autinert subgroups.eninfo:eu-repo/semantics/openAccessArticleQ2Q242313611365WOS:000439014600049348801