Gruppi risolubili dotati di un automorfismo di ordine primo a centralizzante finito
Bollettino dell'Unione Matematica Italiana (2011)
- Volume: 4, Issue: 1, page 123-136
- ISSN: 0392-4041
Access Full Article
top
Abstract
topHow to cite
topBettio, Egle, and Jabara, Enrico. "Gruppi risolubili dotati di un automorfismo di ordine primo a centralizzante finito." Bollettino dell'Unione Matematica Italiana 4.1 (2011): 123-136. <http://eudml.org/doc/290751>.
@article{Bettio2011,
abstract = {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.},
author = {Bettio, Egle, Jabara, Enrico},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {123-136},
publisher = {Unione Matematica Italiana},
title = {Gruppi risolubili dotati di un automorfismo di ordine primo a centralizzante finito},
url = {http://eudml.org/doc/290751},
volume = {4},
year = {2011},
}
TY - JOUR
AU - Bettio, Egle
AU - Jabara, Enrico
TI - Gruppi risolubili dotati di un automorfismo di ordine primo a centralizzante finito
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/2//
PB - Unione Matematica Italiana
VL - 4
IS - 1
SP - 123
EP - 136
AB - 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.
LA - eng
UR - http://eudml.org/doc/290751
ER -
References
top- ENDIMIONI, G., On almost regular automorphisms. Arch. Math. (Basel) 94 (2010), 19-27. Zbl1205.20041MR2581329DOI10.1007/s00013-009-0084-6
- ENDIMIONI, G., Polycyclic group admitting an almost regular automorphism of prime order. J. Algebra, 323 (2010), 3142-3146. Zbl1202.20037MR2629705DOI10.1016/j.jalgebra.2010.03.015
- HARTLEY, B. - MEIXNER, T., Finite soluble groups containing an element of prime order whose centralizer is small. Arch. Math. (Basel) 36 (1981), 211-213. Zbl0447.20014MR620509DOI10.1007/BF01223692
- 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.
- JABARA, E., Automorphisms with finite Reidemeister number in residually finite groups. J. Algebra, 320 (2008), 3671-3679. Zbl1161.20026MR2457715DOI10.1016/j.jalgebra.2008.09.001
- KHUKHRO, E. I., Nilpotent groups and their automorphisms. de Gruyter Expositions in Mathematics, 8. Walter de Gruyter Co., Berlin (1993). Zbl0795.20018MR1224233DOI10.1515/9783110846218
- LENNOX, J. C. - ROBINSON, D. J. S., The theory of infinite soluble groups. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, Oxford (2004). MR2093872DOI10.1093/acprof:oso/9780198507284.001.0001
- ROBINSON, D. J. S., A course in the theory of groups. Second edition. GTM, 80. Springer-Verlag, New York (1996). MR1357169DOI10.1007/978-1-4419-8594-1
- ZAPPA, G., Sugli automorfismi uniformi nei gruppi di Hirsch. Ricerche Mat., 7 (1958), 3-13. MR100632
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.