ON FINITELY GENERATED SOLUBLE NON-HOPFIAN GROUPS, AN APPLICATION TO A PROBLEM OF NEUMANN-Reference-Cited by-同舟云学术

ON FINITELY GENERATED SOLUBLE NON-HOPFIAN GROUPS, AN APPLICATION TO A PROBLEM OF NEUMANN

Published:2007-08 Issue:05n06 Volume:17 Page:1107-1113
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

MIKAELIAN VAHAGN H.¹

Affiliation:

1. Informatics Department, Yerevan State University, Alex-Manoogian 1, Yerevan 37 5025, Armenia

Abstract

Using methods of embeddings of groups, we prove that there is a continuum of soluble non-metanilpotent varieties which contain 3-generator non-Hopfian groups and non-countably many pairwise non-isomorphic finitely generated groups. This provides us with broad sets of groups for which a problem of Neumann has positive answer.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196707004086

Reference10 articles.

1. On some finiteness conditions for Varieties of metanilpotent groups

2. Normal embeddings of p-groups into p-groups

3. Subnormal Embedding Theorems for Groups

4. On Embeddings of Countable Generalized Soluble Groups into Two-Generated Groups

5. An Embedding Construction for Ordered Groups

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Chain groups of homeomorphisms of the interval;Annales scientifiques de l'École normale supérieure;2019

2. On Some Residual Properties of the Verbal Embeddings of Groups;ADV GROUP THEOR APPL;2016

3. Varieties Generated by Wreath Products of Abelian Groups;Journal of Mathematical Sciences;2013-11-08

4. A problem from the kourovka notebook on embeddings of the group $$ \mathbb{Q} $$;Journal of Mathematical Sciences;2012-09-29