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Groups with many normal-by-finite subgroups
Author(s):
Silvana
Franciosi;
Francesco
de Giovanni
Journal:
Proc. Amer. Math. Soc.
125
(1997),
323-327.
MSC (1991):
Primary 20F22
MathSciNet review:
1346971
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Abstract:
A subgroup  of a group  is said to be normal-by-finite if the core  of  in  has finite index in  . In this article groups satisfying the minimal condition on subgroups which are not normal-by-finite and groups with finitely many conjugacy classes of subgroups which are not normal-by-finite are characterized.
References:
- [1]
- B. Amberg, S. Franciosi and F. de Giovanni, Products of Groups, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1992. MR 94h:20001
- [2]
- R. Brandl, S. Franciosi and F. de Giovanni, Groups with finitely many conjugacy classes of non-normal subgroups, Proc. Roy. Irish Acad. Sect. A 95 (1995), 17-27. CMP 1996:6
- [3]
- J. Buckley, J. C. Lennox, B. H. Neumann, H. Smith, and J. Wiegold, Groups with all subgroups normal-by-finite, J. Austral. Math. Soc. Ser. A 59 (1995), 384-398. MR 96h:20076
- [4]
- S. Franciosi and F. de Giovanni, Groups satisfying the minimal condition of non-subnormal subgroups, Proceedings of ``Infinite Groups 1994'', de Gruyter, Berlin, 63-72.
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- [6]
- S. Franciosi, F. de Giovanni, and M. L. Newell, Groups whose subnormal subgroups are normal-by-finite, Comm. Algebra 23 (1995), 5483-5497. MR 96h:20058
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- [8]
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- [9]
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- [11]
- V. P. \v{S}unkov, On the minimality problem for locally finite groups, Algebra and Logic 9 (1970), 137-151. MR 44:295 (Russian original)
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Additional Information:
Silvana
Franciosi
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli ``Federico II'', Complesso Universitario Monte S. Angelo, Via Cintia, I 80126 Napoli, Italy
Francesco
de Giovanni
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli ``Federico II'', Complesso Universitario Monte S. Angelo, Via Cintia, I 80126 Napoli, Italy
Email:
degiova@matna2.dma.unina.it
DOI:
10.1090/S0002-9939-97-03539-9
PII:
S 0002-9939(97)03539-9
Received by editor(s):
May 11, 1995
Communicated by:
Ronald M. Solomon
Copyright of article:
Copyright
1997,
American Mathematical Society
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