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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- [5] P. Hall, On the finiteness of certain soluble groups, Proc. London Math. Soc. (3) 9 (1959), 595-622. Zbl0091.02501
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- [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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