Geodesic
Finite groups with an automorphism of prime order whose fixed points are in the Frattini of a nilpotent subgroup
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 2, pp. 89-92 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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In this paper it is proved that a finite group G with an automorphism \( \alpha \) of prime order r, such that \( C_{G}(\alpha) = 1 \) is contained in a nilpotent subgroup H, with \( (|H|, r) = 1 \), is nilpotent provided that either \( |H| \) is odd or, if \( |H| \) is even, then r is not a Fermât prime. 
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     author = {Gilotti, Anna Luisa},
     title = {Finite groups with an automorphism of prime order whose fixed points are in the {Frattini} of a nilpotent subgroup},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {89--92},
     year = {1990},
     volume = {Ser. 9, 1},
     number = {2},
     zbl = {0728.20016},
     mrnumber = {MR1081388},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1990_9_1_2_a1/}
}
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Gilotti, Anna Luisa. Finite groups with an automorphism of prime order whose fixed points are in the Frattini of a nilpotent subgroup. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 2, pp. 89-92. http://geodesic.mathdoc.fr/item/RLIN_1990_9_1_2_a1/