Let be a fixed odd prime number. In this note we study the class of finite -groups admitting an automorphism of order such that and for all . In this paper we prove that if the derived length of is and is nilpotent of class , then the nilpotency class of is bounded by a function depending only on , and . We prove also that if and is nilpotent of class , then is nilpotent of class at most .
Cite this article
Egle Bettio, Giorgio Busetto, Enrico Jabara, Automorfismi involutori di -gruppi finiti. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 1–15DOI 10.4171/RSMUP/129-1