Abstract
It is shown that if G is a finite p-group with \(p>2\) and \((|Z(G)|, |Z_3(G)|) \in \{ (p, p^4), (p^2, p^5) \}\), then G has a noninner automorphism of order p, where \(Z_3(G)\) is the third member of the upper central series of G. In particular, there exists a noninner automorphism of order p in some families of finite p-groups of coclass 3.
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The authors are grateful to the referee for his valuable suggestions. The paper was revised according to his comments and also the authors would like to thank the Kharazmi University (Iran) for the financial support.
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Communicated by Cheryl E. Praeger.
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Orfi, R., Fouladi, S. Noninner Automorphisms of Order p in Some Finite p-Groups . Bull. Iran. Math. Soc. 44, 1295–1301 (2018). https://doi.org/10.1007/s41980-018-0091-0
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DOI: https://doi.org/10.1007/s41980-018-0091-0