On strongly autinertial groups

Authors : Cansu Betin ONUR

Pages : 1361-1365

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :A subgroup $ X $ of $ G $ is said to be inert under automorphisms insert ignore into journalissuearticles values(autinert); if $ |X : X^\alpha \cap X | $ is finite for all $ \alpha \in Autinsert ignore into journalissuearticles values(G);$ and it is called strongly autinert if $ |:X | $ is finite for all $ \alpha \in Autinsert ignore into journalissuearticles values(G);.$ A group is called strongly autinertial if all subgroups are strongly autinert. In this article, the strongly autinertial groups are studied. We characterize such groups for a finitely generated case. Namely, we prove that a finitely generated group $ G $ is strongly autinertial if and only if one of the following hold:\vs{-2mm} \begin{itemize} \item[i);] $ G $ is finite;\vs{-2mm} \item[ii);] $ G= \langle a \rangle \ltimes F $ where $ F $ is a finite subgroup of $ G $ and $ \langle a \rangle $ is a torsion-free subgroup of $ G. $ \end{itemize}\vs{-2mm} Moreover, in the preliminary part, we give basic results on strongly autinert subgroups.
Keywords : Autinert subgroups, inertial groups, FC groups, VTA groups, virtually cyclic groups