On groups with countably many maximal subgroups-Reference-Cited by-同舟云学术

On groups with countably many maximal subgroups

Published:2017-10-17 Issue:2 Volume:21 Page:253-271
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Arikan Ahmet¹,Cutolo Giovanni²,Robinson Derek J. S.³

Affiliation:

1. Department of Mathematics and Science Education , Gazi University , 06500 Teknikokullar , Ankara , Turkey

2. Dipartimento di Matematica e Applicazioni , Università di Napoli Federico II , I-80126 Naples , Italy

3. Department of Mathematics , University of Illinois at Urbana-Champaign , Urbana , IL 61801 , USA

Abstract

Abstract The object of this work is to find classes of groups which possess only countably many maximal subgroups. Modules with countably many maximal submodules and group rings having countably many maximal right ideals are also investigated. Examples of soluble groups with uncountably many maximal subgroups are described.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference17 articles.

1. R. Baer, Irreducible groups of automorphisms of abelian groups, Pacific J. Math. 14 (1964), 385–406.

2. S. N. Černikov, On the theory of complete groups (in Russian), Mat. Sb. (N.S.) 22(64) (1948), 319-348

3. translation in Amer. Math. Soc. Transl. Ser. 1 56 (1951), 3-49.

4. Y. de Cornulier, MathOverflow, 2016, mathoverflow.net/questions/249071/.

5. G. Cutolo and H. Smith, Groups with countably many subgroups, J. Algebra 448 (2016), 399–417.

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