Groups with many normal-by-finite subgroups

Authors:
Silvana Franciosi and Francesco de Giovanni

Journal:
Proc. Amer. Math. Soc. **125** (1997), 323-327

MSC (1991):
Primary 20F22

DOI:
https://doi.org/10.1090/S0002-9939-97-03539-9

MathSciNet review:
1346971

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Abstract | References | Similar Articles | Additional Information

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.

**[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.**[5]**S. Franciosi and F. de Giovanni,*Groups satisfying the minimal condition on certain non-normal subgroups*, Proceedings of ``Groups-Korea 1994'', de Gruyter, Berlin, 107-118.**[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****[7]**R. E. Phillips and J. S. Wilson,*On certain minimal conditions for infinite groups*, J. Algebra**51**(1978), 41-68. MR**58:11126****[8]**D. J. S. Robinson,*Finiteness Conditions and Generalized Soluble Groups*. Parts I, II, Springer, Berlin, 1972. MR**48:111314,111315****[9]**H. Smith,*Groups with finitely many conjugacy classes of subgroups with large subnormal defect*, Glasgow Math. J.**37**(1995), 69-71. MR**96a:22048****[10]**H. Smith and J. Wiegold,*Locally graded groups with all subgroups normal-by-finite*, J. Austral. Math. Soc. Ser. A**60**(1996), 222-227. CMP**1996:8****[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:
https://doi.org/10.1090/S0002-9939-97-03539-9

Received by editor(s):
May 11, 1995

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1997
American Mathematical Society