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Noninner automorphisms of finite p-groups leaving the center elementwise fixed | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 2، شماره 4، اسفند 2013، صفحه 17-20 اصل مقاله (343.22 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2761 | ||
| نویسندگان | ||
| Alireza Abdollahi* ؛ S. Mohsen Ghoraishi | ||
| University of Isfahan | ||
| چکیده | ||
| A longstanding conjecture asserts that every finite nonabelian $p$-group admits a noninner automorphism of order $p$. Let $G$ be a finite nonabelian $p$-group. It is known that if $G$ is regular or of nilpotency class $2$ or the commutator subgroup of $G$ is cyclic, or $G/Z(G)$ is powerful, then $G$ has a noninner automorphism of order $p$ leaving either the center $Z(G)$ or the Frattini subgroup $\Phi(G)$ of $G$ elementwise fixed. In this note, we prove that the latter noninner automorphism can be chosen so that it leaves $Z(G)$ elementwise fixed. | ||
| کلیدواژهها | ||
| Noninner automorphism؛ finite p-groups؛ the center | ||
| مراجع | ||
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