Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T11:51:52.148Z Has data issue: false hasContentIssue false
  • English
  • Français

Finitary and Artinian-finitary groups

Published online by Cambridge University Press:  01 September 2007

B. A. F. WEHRFRITZ
B. A. F. WEHRFRITZ*
Affiliation:
School of Mathematical Sciences, Queen Mary College, University of London, Mile End Road, London E1 4NS.
Get access Rights & Permissions [Opens in a new window]

Abstract

Let M be a module over the ring R. The finitary automorphism group of M over R isand the Artinian-finitary automorphism group of M over R isWe continue our study begun in [9] and [12] of the relationship between these two in some ways similar, but actually quite different types of automorphism group. Our study here involves the generalized finitary group embeds into some finitely generated R-module which does not fit our earlier pattern of generalized finitary groups as described in [8].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 291 - 305
Copyright
Copyright © Cambridge Philosophical Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Camps, R. and Facchini, A.. The Prüfer rings that are endomorphism rings of Artinian modules. Comm. Algebra 22 (1994), 3133–3157.CrossRefGoogle Scholar
[2]Facchini, A.. Loewy and Artinian modules over commutative rings. Ann. Mat. Pura Appl. 128 (1981), 359–374.CrossRefGoogle Scholar
[3]Gruenberg, K. W.. The upper central series in soluble groups. Illinois J. Math. 5 (1961), 436–466.CrossRefGoogle Scholar
[4]Sharpe, D. W. and Vámos, P.. Injective Modules (Cambridge University Press, 1972).Google Scholar
[5]Shirvani, M. and Wehrfritz, B. A. F.. Skew Linear Groups (Cambridge University Press, 1986).Google Scholar
[6]Wehrfritz, B. A. F.. Locally soluble finitary skew linear groups. J. Algebra 160 (1993), 226–241.CrossRefGoogle Scholar
[7]Wehrfritz, B. A. F.. Locally soluble primitive finitary skew linear groups. Comm. Algebra 23 (1995), 803–817.CrossRefGoogle Scholar
[8]Wehrfritz, B. A. F.. J. Algebra 247 (2002), 707–727.CrossRefGoogle Scholar
[9]Wehrfritz, B. A. F.. Finitary and Artinian-finitary groups over the integers Z. Ukrain. Math. J. 54 (2002) 924–936.CrossRefGoogle Scholar
[10]Wehrfritz, B. A. F.. Nilpotence in finitary groups over commutative rings. Comm. Algebra 30 (2002), 1417–1435.CrossRefGoogle Scholar
[11]Wehrfritz, B. A. F.. Artinian-finitary groups over commutative rings. Illinois J. Math. 47 (2003), 551–565.CrossRefGoogle Scholar
[12]Wehrfritz, B. A. F.. Finitary and Artinian-finitary groups over commutative rings. J. Group Theory 7 (2004), 243–253.CrossRefGoogle Scholar
[13]Wehrfritz, B. A. F.. Artinian-finitary groups over commutative and non-commutative rings. J. London Math. Soc. 70 (2004), 325–340.CrossRefGoogle Scholar