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On noninner automorphisms of finite $p$-groups that fix the center elementwise | ||
| International Journal of Group Theory | ||
| مقاله 1، دوره 8، شماره 1، خرداد 2019، صفحه 1-9 اصل مقاله (212.4 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2018.108082.1457 | ||
| نویسنده | ||
| S. Mohsen Ghoraishi* | ||
| Shahid Chamran University | ||
| چکیده | ||
| In this paper we show that every finite nonabelian $p$-group $G$ in which the Frattini subgroup $\Phi(G)$ has order $\leq p^5$ admits a noninner automorphism of order $p$ leaving the center $Z(G)$ elementwise fixed. As a consequence it follows that the order of a possible counterexample to the conjecture of Berkovich is at least $p^8$. | ||
| کلیدواژهها | ||
| $p$-groups؛ automorphisms؛ noninner automorphisms | ||
| مراجع | ||
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