JournalsrsmupVol. 129pp. 1–15

Automorfismi involutori di pp-gruppi finiti

  • Egle Bettio

    Liceo Scientifico G.B. Benedetti, Venezia, Italy
  • Giorgio Busetto

    Università di Ca' Foscari, Mestre (Venezia), Italy
  • Enrico Jabara

    Università di Ca' Foscari, Venezia, Italy
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Abstract

Let pp be a fixed odd prime number. In this note we study the class of finite pp-groups GG admitting an automorphism φ{\varphi} of order 22 such that G=g1gφgGG=\langle \, g^{-1}g^{{\varphi} } \mid g \in G \, \rangle and (g1gφ)p=1(\kern 0.5pt g^{-1}g^{{\varphi} })^{\kern 1pt p}=1 for all gGg \in G. In this paper we prove that if the derived length of GG is dd and CG(φ)C_{G}({\varphi} ) is nilpotent of class cc, then the nilpotency class of GG is bounded by a function depending only on dd, cc and pp. We prove also that if p=3p=3 and CG(φ)C_{G}({\varphi} ) is nilpotent of class cc, then GG is nilpotent of class at most 2c+12c+1.

Cite this article

Egle Bettio, Giorgio Busetto, Enrico Jabara, Automorfismi involutori di pp-gruppi finiti. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 1–15

DOI 10.4171/RSMUP/129-1