Abstract.
Let G be a group and let Aut c (G) be the group of central automorphisms of G. Let \({{C_{{\rm Aut}_{c}(G)}}(Z(G))}\) be the set of all central automorphisms of G fixing Z(G) elementwise. In this paper we prove that if G is a finite p-group, then \({C_{{\rm Aut}_{c}(G)}}(Z(G))\) = Inn(G) if and only if G is abelian or G is nilpotent of class 2 and Z(G) is cyclic.
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This work was supported in part by the Center of Excellence for Mathematics, University of Isfahan, Iran.
Received: 30 October 2006
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Attar, M.S. On central automorphisms that fix the centre elementwise. Arch. Math. 89, 296–297 (2007). https://doi.org/10.1007/s00013-007-2205-4
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DOI: https://doi.org/10.1007/s00013-007-2205-4