A note on central automorphisms that fix the center elementwise

Mehdi Shabani-Attar ()
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Mehdi Shabani-Attar: Payame Noor University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 150-155

Abstract: Abstract Let p be a prime number, $$\text{ Inn }(G)$$ Inn ( G ) the group of inner automorphisms of G and $$\text{ C}_{Aut_{c}(G)}(Z(G))$$ C A u t c ( G ) ( Z ( G ) ) be the set of all central automorphisms of G fixing Z(G) elementwise. In this article, we characterize all finite p-groups G for which $$[\text{ C}_{Aut_{c}(G)}(Z(G)):\text{ Inn }(G)]=p^3$$ [ C A u t c ( G ) ( Z ( G ) ) : Inn ( G ) ] = p 3 or $$p^4.$$ p 4 .

Keywords: Central automorphisms; Finite p-groups; 20D45; 20D15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00464-5

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