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On Finite p-Groups Whose Central Automorphisms Are All nth Class-Preserving

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Abstract

Let G be a finite non-abelian p-group, where p is a prime. An automorphism \(\alpha \) of G is called an nth class-preserving if for each \(x\in G\), there exists an element \(g_x\in \gamma _n(G)\) such that \(\alpha (x)=g_x^{-1}xg_x\). An automorphism \(\alpha \) of G is called a central automorphism if \(x^{-1}\alpha (x)\in Z(G)\) for all \(x\in G\). Let \({{\,\mathrm{Aut}\,}}_{c}^n(G)\) and \({{\,\mathrm{Autcent}\,}}(G)\), respectively, denote the group of all nth class-preserving and central automorphisms of G. We give necessary and sufficient conditions for a finite p-group G of class \(n+1\) such that \({{\,\mathrm{Aut}\,}}_{c}^n(G)={{\,\mathrm{Autcent}\,}}(G)\).

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Correspondence to Rohit Garg.

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Garg, R. On Finite p-Groups Whose Central Automorphisms Are All nth Class-Preserving. Bull. Iran. Math. Soc. 46, 417–423 (2020). https://doi.org/10.1007/s41980-019-00266-8

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  • DOI: https://doi.org/10.1007/s41980-019-00266-8

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