# On residually finite groups and their generalizations

Colloquium Mathematicae (1999)

- Volume: 79, Issue: 1, page 25-35
- ISSN: 0010-1354

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topStrojnowski, Andrzej. "On residually finite groups and their generalizations." Colloquium Mathematicae 79.1 (1999): 25-35. <http://eudml.org/doc/210625>.

@article{Strojnowski1999,

abstract = {The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions asked in [1] and [2].},

author = {Strojnowski, Andrzej},

journal = {Colloquium Mathematicae},

keywords = {residually finite groups; finite embedding property; soluble groups},

language = {eng},

number = {1},

pages = {25-35},

title = {On residually finite groups and their generalizations},

url = {http://eudml.org/doc/210625},

volume = {79},

year = {1999},

}

TY - JOUR

AU - Strojnowski, Andrzej

TI - On residually finite groups and their generalizations

JO - Colloquium Mathematicae

PY - 1999

VL - 79

IS - 1

SP - 25

EP - 35

AB - The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions asked in [1] and [2].

LA - eng

KW - residually finite groups; finite embedding property; soluble groups

UR - http://eudml.org/doc/210625

ER -

## References

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- [3] S. Dăscălescu, C. Năstăsescu, A. del Rio and F. Van Oystayen, Gradings of finite support. Application to injective objects, J. Pure Appl. Algebra 107 (1996), 193-206. Zbl0859.16036
- [4] E. Formanek, Idempotents in Noetherian group rings, Canad. J. Math. 15 (1973), 366-369.
- [5] P. Hall, On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595-622. Zbl0091.02501
- [6] I. Kaplansky, Problems in the theory of rings, in: Report of a Conference on Linear Algebras, National Acad. Sci., Washington, 1957, 1-3. Zbl0095.25602
- [7] P. A. Linnel, Decomposition of augmentation ideals and relation modules, Proc. London Math. Soc. 47 (1983), 83-127.
- [8] A. V. Mikhalev and A. E. Zalesskiĭ, Group Rings, Nauka, Moscow, 1973 (in Russian).
- [9] D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin, 1972. Zbl0243.20032
- [10] A. Strojnowski, On Bass' 'Strong Conjecture' about projective modules, J. Pure Appl. Algebra 62 (1989), 195-198. Zbl0688.16013
- [11] J. S. Wilson Embedding theorems for residually finite groups, Math. Z. 174 (1980), 149-157. Zbl0424.20028

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