Let A be an elementary abelian group of order pk with k ≥ 3 acting on a finite p′-group G. The following results are proved. If γk−2(CG(a)) is nilpotent of class at most c for any a ∈ A#, then γk−2(G) is nilpotent and has {c, k, p}-bounded nilpotency class. If, for some integer d such that 2d + 2 ≤ k, the dth derived group of CG (a) is nilpotent of class at most c for any a ∈ A#, then the dth derived group G(d) is nilpotent and has {c, k, p}-bounded nilpotency class.

Centralizers of coprime automorphisms of finite groups / Acciarri, C; Shumyatsky, P.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 193:2(2014), pp. 317-324. [10.1007/s10231-012-0274-x]

Centralizers of coprime automorphisms of finite groups

ACCIARRI C;
2014-01-01

Abstract

Let A be an elementary abelian group of order pk with k ≥ 3 acting on a finite p′-group G. The following results are proved. If γk−2(CG(a)) is nilpotent of class at most c for any a ∈ A#, then γk−2(G) is nilpotent and has {c, k, p}-bounded nilpotency class. If, for some integer d such that 2d + 2 ≤ k, the dth derived group of CG (a) is nilpotent of class at most c for any a ∈ A#, then the dth derived group G(d) is nilpotent and has {c, k, p}-bounded nilpotency class.
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Centralizers of coprime automorphisms of finite groups / Acciarri, C; Shumyatsky, P.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 193:2(2014), pp. 317-324. [10.1007/s10231-012-0274-x]
Acciarri, C; Shumyatsky, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1255534
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