A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. In this paper, we give a lower bound for the coclass of finite nonabelian p-groups G having no noninner automorphism of order p leaving the Frattini subgoup \(\Phi (G)\) elementwise fixed. As a consequence, the verification of the conjecture is reduced to the case of finite nonabelian p-groups G in which the coclass of G is greater than the minimum number of generators of G.

中文翻译：

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受限协类的有限 p 群的 p 阶非内自同构

一个长期存在的猜想断言，每个有限非阿贝尔p群都承认p阶的非内自同构。在本文中，我们给出了一个下界有限非交换的组件类p -基团ģ具有顺序的无noninner构p离开帝尼subgoup \（\披（G）\）的elementwise固定。其结果是，该猜想的验证被减小到有限非交换的情况下，p -基团ģ其中的组件类ģ比的发电机的最小数目越大ģ。