Geodesic
On locally finite groups and the centralizers of automorphisms
Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 3, pp. 731-736.

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Sia $p$ un primo, e $A$ un gruppo abeliano elementare di ordine $p^{2}$ che agisce sul $p'$-gruppo localmente finito $G$. Supponiamo che esista un intero positivo $m$ tale che $[C_{G}(a), \underbrace{C_{G}(b), \ldots , C_{G}(b)}_{m}]=1$ per ogni $a, b\in A^{\sharp}$. In questo articolo si dimostra che $G$ è nilpotente, con classe di nilpotenza limitata da una funzione che dipende solo da $p$ e $m$. 
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Shumyatsky, Pavel. On locally finite groups and the centralizers of automorphisms. Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 3, pp. 731-736. http://geodesic.mathdoc.fr/item/BUMI_2001_8_4B_3_a11/

[1] Chong-Yun Chao, Some characterizations of nilpotent Lie algebras, Math. Z., 103 (1968), 40-42. | MR | Zbl

[2] D. Gorenstein, Finite groups, New York, Evanston, London: Harper and Row, 1968. | MR | Zbl

[3] H. Hall, Some sufficient conditions for a group to be nilpotent, Illinois J. Math., 2 (1958), 595-622. | fulltext mini-dml | MR | Zbl

[4] O. H. Kegel-B. A. F. Wehrfritz, Locally finite groups, North Holland, Amsterdam, 1973. | MR | Zbl

[5] E. I. Khukhro-P. Shumyatsky, On fixed points of automorphisms of Lie rings and locally finite groups, Algebra and Logic, 34 (1995), 395-405. | MR | Zbl

[6] V. A. Kreknin, Solvability of Lie algebras with a regular automorphism of finite period, Soviet Math. Dokl., 4 (1963), 683-685. | MR | Zbl

[7] P. Shumyatsky, On periodic soluble groups and the fixed point groups of operators, Comm. Algebra, 20(10) (1992), 2815-2820. | MR | Zbl

[8] P. Shumyatsky, On periodic solvable groups having automorphisms with nilpotent fixed point groups, Israel Math. J., 87 (1994), 111-116. | MR | Zbl

[9] J. N. Ward, Automorphisms of finite groups and their fixed-point subgroups, J. Austral. Math. Soc., 9 (1969), 467-477. | MR | Zbl

[10] J. N. Ward, On finite groups admitting automorphisms with nilpotent fixed-point group, Bull. Austral. Math. Soc., 5 (1971), 281-282. | MR | Zbl

[11] J. N. Ward, On groups admitting a noncyclic abelian automorphism group, Bull. Austral. Math. Soc., 9 (1973), 363-366. | MR | Zbl