PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 79 | 1 | 25-35
Tytuł artykułu

On residually finite groups and their generalizations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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].
Słowa kluczowe
Rocznik
Tom
79
Numer
1
Strony
25-35
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-01-17
poprawiono
1998-05-06
Twórcy
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • [1] H. Bass, Euler characteristics and characters of discrete groups, Invent. Math. 35 (1976), 155-196.
  • [2] S. Dăscălescu, A note on groups with the finite embedding property, Proc. Internat. Conf. on Group Theory (Timişoara, 1992), An. Univ. Timişoara Ser. Ştiinţ. Mat. 1993, special issue, 43-45.
  • [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.
  • [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.
  • [6] I. Kaplansky, Problems in the theory of rings, in: Report of a Conference on Linear Algebras, National Acad. Sci., Washington, 1957, 1-3.
  • [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.
  • [10] A. Strojnowski, On Bass' 'Strong Conjecture' about projective modules, J. Pure Appl. Algebra 62 (1989), 195-198.
  • [11] J. S. Wilson Embedding theorems for residually finite groups, Math. Z. 174 (1980), 149-157.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv79z1p25bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.