Let G be a finite non-abelian p-group and let \(W(G)/Z(G)=\Omega _1(Z_2(G)/Z(G))\). A longstanding conjecture asserts that G admits a non-inner automorphism of order p. We confirm the conjecture in case Z(G) is not cyclic and W(G) is non-abelian.

中文翻译：

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具有非循环中心的有限 p 群具有 p 阶非内自同构

令G为有限非阿贝尔p群，并令\(W(G)/Z(G)=\Omega _1(Z_2(G)/Z(G))\)。一个长期存在的猜想断言G承认p阶的非内自同构。我们确认了在Z ( G ) 不是循环且W ( G ) 是非阿贝尔的情况下的猜想。