Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-19T11:12:21.809Z Has data issue: false hasContentIssue false
  • English
  • Français

Some finiteness conditions concerning intersections of conjugates of subgroups

Published online by Cambridge University Press:  18 May 2009

John C. Lennox ,
Patrizia Longobardi ,
Mercede Maj ,
Howard Smith  and
James Wiegold
John C. Lennox
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Cardiff CF2 4AG, Wales
Patrizia Longobardi
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi Di Napoli, Monte S. Angelo—Via Cintia, 80126 Napoli, Italy
Mercede Maj
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi Di Napoli, Monte S. Angelo—Via Cintia, 80126 Napoli, Italy
Howard Smith
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg PA 17837, U.S.A.
James Wiegold
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Cardiff CF2 4AG, Wales
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [3], a group G was said to be a CF-group if, for every subgroup H of G, H/CoreGH is finite. It was shown there that a locally finite CF-group G is abelian-by-finite and that there is a bound for the indices |H: CoreGH| as H runs through all subgroups of G. (Groups for which such a bound exists were referred to in [3] as BCF-groups.) The CF-property was further investigated in [10], one of the main results there being that nilpotent CF-groups are (again) abelian-by-finite and BCF. In the present paper, we shall discuss the CF-property in conjunction with some related properties, which are defined as follows.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 3 , September 1995 , pp. 327 - 335
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Adian, S. I., The problem of Burnside and identities in groups, (Nauka, 1975) (Russian). (Translation by Lennox, J. C. and Wiegold, J., (Springer-Verlag 1979)).CrossRefGoogle Scholar
2.Baumslag, G., Wreath products and p-groups, Proc. Cambridge Phil. Soc. 55 (1959), 224–231.CrossRefGoogle Scholar
3.Buckley, J. T., Lennox, J. C., Neumann, B. H., Smith, H. and Wiegold, J., Groups with all subgroups normal-by-finite, J. Australian Math. Soc. (to appear).Google Scholar
4.Eremin, I.I., Groups with finite classes of conjugate abelian subgroups, Dokl. Akad. Nauk. SSSR (N.S.) 118 (1958), 223–224.Google Scholar
5.Hall, P. and Kulatilaka, C. R., A property of locally finite groups, J. London Math. Soc. 39 (1964), 235–239.CrossRefGoogle Scholar
6.Neumann, B. H., Groups with finite classes of conjugate subgroups, Math. Z. 63 (1955), 76–96.CrossRefGoogle Scholar
7.Ol'shanskii, A. Yu., Geometry of defining relations in groups, (Nauka, 1989).Google Scholar
8.Robinson, D. J. S., Finiteness conditions and generalized soluble groups, (Springer-Verlag 1972).CrossRefGoogle Scholar
9.Rozhkov, A. V., On subgroups of infinite finitely generated p-groups, Mat. Sb. 129 (171) (1986) (= Math. USSR Sbomik 57 (1987), No. 2).Google Scholar
10.Smith, H. and Wiegold, J., Locally graded groups with all subgroups normal-by-finite, J. Austral. Math. Soc., to appear.Google Scholar
11.Zel'manov, E. I., Solution of the restricted Burnside problem for groups of odd exponent, Izv. Akad. Nauk. SSR Ser. Mat. 54 (1990), 42–59.Google Scholar
12.Zel'manov, E. I, Solution of the restructed Burnside problem for 2-groups, Mat. Sb. 182 (1991), 568–592.Google Scholar