Let p be a fixed odd prime number. In this note we study the class of finite p-groups G admitting an automorphism ϕ of order 2 such that G=< g^-1g^ϕ |g∈G〉 and (g^-1 g^ϕ )^p =1 for all g∈G. In this paper we prove that if the derived length of G is d and C G (ϕ) is nilpotent of class c, then the nilpotency class of G is bounded by a function depending only on d,c and p. We prove also that if p=3 and C G (ϕ) is nilpotent of class c, then G is nilpotent of class at most 2c+1.

Automorfismi involutori di p-gruppi finiti.

BUSETTO, Giorgio;JABARA, Enrico
2013-01-01

Abstract

Let p be a fixed odd prime number. In this note we study the class of finite p-groups G admitting an automorphism ϕ of order 2 such that G=< g^-1g^ϕ |g∈G〉 and (g^-1 g^ϕ )^p =1 for all g∈G. In this paper we prove that if the derived length of G is d and C G (ϕ) is nilpotent of class c, then the nilpotency class of G is bounded by a function depending only on d,c and p. We prove also that if p=3 and C G (ϕ) is nilpotent of class c, then G is nilpotent of class at most 2c+1.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/37707
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