Volume 8, Issue 1 (Vol. 8,No. 1, 2022)
mmr 2022, 8(1): 215-223 |
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Faramarzi Salles A. A relation between infinite subsets and exterior center in groups. mmr 2022; 8 (1) :215-223
URL: http://mmr.khu.ac.ir/article-1-3060-en.html
URL: http://mmr.khu.ac.ir/article-1-3060-en.html
Damghan University , faramarzi@du.ac.ir
Abstract: (653 Views)
Let G be a group. Neumann to answer a question of Paul Erdos proved that every infinite subset of G has two different comuting elements if and only if G is center-by-finite. In this paper, we deal with Erdoschr('39')s question in different aspect and we show that every infinite subset X of G has two different elements x and y such that x^y=1 if and only if the exterior center of G ihas finite index.
Keywords: Problem of Paul Erdös, Infinite groups, 〖FC〗^˄- group, Central- by- finite, Exterior abelian, Exterior center of group.
Type of Study: S |
Subject:
alg
Received: 2020/03/8 | Revised: 2022/11/15 | Accepted: 2020/11/23 | Published: 2022/05/14 | ePublished: 2022/05/14
Received: 2020/03/8 | Revised: 2022/11/15 | Accepted: 2020/11/23 | Published: 2022/05/14 | ePublished: 2022/05/14
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