Gruppi risolubili dotati di un automorfismo di ordine primo a centralizzante finito
Bettio, Egle ; Jabara, Enrico
Bollettino dell'Unione Matematica Italiana, Tome 4 (2011), p. 123-136 / Harvested from Biblioteca Digitale Italiana di Matematica
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In this paper we prove that a solvable, finitely generated group G of finite torsion-free rank admitting a quasi regular automorphism of prime order is virtually nilpotent. We also prove that the hypothesis that G is finitely generated can be omitted if G is a minimax group.

Publié le : 2011-02-01
@article{BUMI_2011_9_4_1_123_0,
     author = {Egle Bettio and Enrico Jabara},
     title = {Gruppi risolubili dotati di un automorfismo di ordine primo a centralizzante finito},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4},
     year = {2011},
     pages = {123-136},
     zbl = {1247.20043},
     mrnumber = {2797469},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2011_9_4_1_123_0}
}

Bettio, Egle; Jabara, Enrico. Gruppi risolubili dotati di un automorfismo di ordine primo a centralizzante finito. Bollettino dell'Unione Matematica Italiana, Tome 4 (2011) pp. 123-136. http://gdmltest.u-ga.fr/item/BUMI_2011_9_4_1_123_0/

[1] Endimioni, G., On almost regular automorphisms. Arch. Math. (Basel) 94 (2010), 19-27. | MR 2581329 | Zbl 1205.20041

[2] Endimioni, G., Polycyclic group admitting an almost regular automorphism of prime order. J. Algebra, 323 (2010), 3142-3146. | MR 2629705 | Zbl 1202.20037

[3] Hartley, B. - Meixner, T., Finite soluble groups containing an element of prime order whose centralizer is small. Arch. Math. (Basel) 36 (1981), 211-213. | MR 620509 | Zbl 0447.20014

[4] Jabara, E., Una nota sui gruppi dotati di un automorfismo uniforme di ordine potenza di un primo. Rend. Sem. Mat. Univ. Padova, 84 (1990), 217-221.

[5] Jabara, E., Automorphisms with finite Reidemeister number in residually finite groups. J. Algebra, 320 (2008), 3671-3679. | MR 2457715 | Zbl 1161.20026

[6] Khukhro, E. I., Nilpotent groups and their automorphisms. de Gruyter Expositions in Mathematics, 8. Walter de Gruyter Co., Berlin (1993). | MR 1224233 | Zbl 0795.20018

[7] Lennox, J. C. - Robinson, D. J. S., The theory of infinite soluble groups. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, Oxford (2004). | MR 2093872

[8] Robinson, D. J. S., A course in the theory of groups. Second edition. GTM, 80. Springer-Verlag, New York (1996). | MR 1357169

[9] Zappa, G., Sugli automorfismi uniformi nei gruppi di Hirsch. Ricerche Mat., 7 (1958), 3-13. | MR 100632