Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T07:02:12.998Z Has data issue: false hasContentIssue false
  • English
  • Français

GROUPS IN WHICH NORMAL CLOSURES OF ELEMENTS HAVE BOUNDEDLY FINITE RANK

Published online by Cambridge University Press:  01 May 2009

PATRIZIA LONGOBARDI ,
MERCEDE MAJ  and
HOWARD SMITH
PATRIZIA LONGOBARDI
Affiliation:
Dipartimento di Matematica e Informatica, Universitá di Salerno, Via Ponte don Melillo, 84084 Fisciano (Salerno), Italy e-mail: plongobardi@unisa.it, mmaj@unisa.it
MERCEDE MAJ
Affiliation:
Dipartimento di Matematica e Informatica, Universitá di Salerno, Via Ponte don Melillo, 84084 Fisciano (Salerno), Italy e-mail: plongobardi@unisa.it, mmaj@unisa.it
HOWARD SMITH
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA e-mail: howsmith@bucknell.edu
Rights & Permissions [Opens in a new window]

Abstract

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.

It is proved that if the normal closure of every element of a group G has rank at most r, then the derived subgroup of G has r-bounded rank.

Keywords

20F24
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009 , pp. 341 - 345
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Černikov, N. S., A theorem on groups of special rank [translated], Ukrainian Math. J. 42 (1990), 855–861.CrossRefGoogle Scholar
2.Lubotzky, A. and Mann, A., Residually finite groups of finite rank, Math. Proc. Camb. Phil. Soc. 106 (1989), 385–388.CrossRefGoogle Scholar
3.Neumann, B. H., Groups covered by permutable subsets, J. Lond. Math. Soc. 29 (1954), 227–242.Google Scholar
4.Neumann, B. H., Groups with finite classes of conjugate subgroups, Math. Z. 63 (1955), 76–96.CrossRefGoogle Scholar
5.Robinson, D. J. S., Finiteness conditions and generalized soluble groups, vol. 2 (Springer, Berlin Heidelberg, New York, 1972).CrossRefGoogle Scholar
6.Robinson, D. J. S., A course in the theory of groups (Springer, Berlin Heidelberg, New York, 1982).CrossRefGoogle Scholar
7.Segal, D. and Shalev, A., On groups with bounded conjugacy classes, Quart. J. Math. Oxford Ser. 50 (1999), 505–516.CrossRefGoogle Scholar
8.Smith, H., A finiteness condition on normal closures of cyclic subgroups, Math. Proc. R. Irish Acad. 99A (1999), 179–183.Google Scholar