Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms
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 ab...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/4923433 |
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| author | Esmat Alamshahi Mohammad Reza R. Moghaddam Mohammad Amin Rostamyari |
| author_facet | Esmat Alamshahi Mohammad Reza R. Moghaddam Mohammad Amin Rostamyari |
| author_sort | Esmat Alamshahi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c9dc32c633f245c4a55087eacf0d2366 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c9dc32c633f245c4a55087eacf0d23662025-02-03T06:11:19ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4923433Finite Groups Which Are the Union of Autocentralizers of Some AutomorphismsEsmat Alamshahi0Mohammad Reza R. Moghaddam1Mohammad Amin Rostamyari2Department of MathematicsDepartment of MathematicsDepartment of MathematicsLet 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.http://dx.doi.org/10.1155/2022/4923433 |
| spellingShingle | Esmat Alamshahi Mohammad Reza R. Moghaddam Mohammad Amin Rostamyari Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms Journal of Mathematics |
| title | Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms |
| title_full | Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms |
| title_fullStr | Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms |
| title_full_unstemmed | Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms |
| title_short | Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms |
| title_sort | finite groups which are the union of autocentralizers of some automorphisms |
| url | http://dx.doi.org/10.1155/2022/4923433 |
| work_keys_str_mv | AT esmatalamshahi finitegroupswhicharetheunionofautocentralizersofsomeautomorphisms AT mohammadrezarmoghaddam finitegroupswhicharetheunionofautocentralizersofsomeautomorphisms AT mohammadaminrostamyari finitegroupswhicharetheunionofautocentralizersofsomeautomorphisms |