On noninner automorphisms of finite $p$-groups that fix the center elementwise
عنوان مقاله: On noninner automorphisms of finite $p$-groups that fix the center elementwise
شناسه ملی مقاله: JR_THEGR-8-1_001
منتشر شده در در سال 1398
شناسه ملی مقاله: JR_THEGR-8-1_001
منتشر شده در در سال 1398
مشخصات نویسندگان مقاله:
S. Mohsen Ghoraishi - Shahid Chamran University
خلاصه مقاله:
S. Mohsen Ghoraishi - Shahid Chamran University
In this paper we show that every finite nonabelian $p$-group $G$ in which the Frattini subgroup $\Phi(G)$ has order $\leq p^۵$ 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 $p^۸$.
کلمات کلیدی: $p$-groups, automorphisms, noninner automorphisms
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1194957/