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Groups with some central automorphisms fixing the central kernel quotient | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 165-177 اصل مقاله (512.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19047.1220 | ||
| نویسنده | ||
| Rasoul Soleimani* | ||
| Department of Mathematics, Payame Noor University (PNU), Iran | ||
| چکیده | ||
| Let $G$ be a group. An automorphism $\alpha$ of a group $G$ is called a central automorphism, if $x^{-1}x^{\alpha}\in Z(G)$ for all $x\in G$. Let $L_c(G)$ be the central kernel of $G$, that is the set of elements of $G$ fixed by all central automorphisms of $G$ and $Aut_{L_c}(G)$ denote the group of all central automorphisms of $G$ fixing $G/L_c(G)$ element-wise. In the present paper, we investigate the properties of such automorphisms. Moreover, a full classification of $p$-groups $G$ of order at most $p^5$ where $Aut_{L_c}(G)=Inn(G)$ is also given. | ||
| کلیدواژه‌ها | ||
| Automorphism group؛ central kernel؛ central autocommutator | ||
| مراجع | ||
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