Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms

Esmat Alamshahi, Mohammad Reza R. Moghaddam, Mohammad Amin Rostamyari and Naihuan Jing

Journal of Mathematics, 2022, vol. 2022, 1-6

Abstract: Let α be an automorphism of a given group G; then, CGα=g∈G|αg=g is called the autocentralizer of α in G. In this work, we study finite groups G, which can be written as the union of autocentralizers of some automorphisms of G. In particular, if a group G is 5-A-centralizers, then we determine the absolute central quotient G/LG of G, where A=AutG. Finally, it is shown that autocommutative property of a group is equivalent to the one, in which every A-centralizer of its nontrivial elements is abelian.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4923433

DOI: 10.1155/2022/4923433

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