Normal nearness subgroups
- Authors
- Öztürk, Mehmet Ali; Tekin, Özlem; Jun, Young Bae
- Issue Date
- Jan-2024
- Publisher
- Marcel Dekker Inc.
- Keywords
- Groups; near sets; nearness groups; nearness subgroups; normal nearness subgroups; quotient nearness groups; weak nearness approximation spaces
- Citation
- Communications in Algebra, v.52, no.1, pp 102 - 115
- Pages
- 14
- Indexed
- SCIE
SCOPUS
- Journal Title
- Communications in Algebra
- Volume
- 52
- Number
- 1
- Start Page
- 102
- End Page
- 115
- URI
- https://scholarworks.gnu.ac.kr/handle/sw.gnu/68728
- DOI
- 10.1080/00927872.2023.2234037
- ISSN
- 0092-7872
1532-4125
- Abstract
- In 2022, Öztürk defined the nearness equivalence classes and nearness cosets of the nearness groups (see [10]). Furthermore, he showed a nearness group G induced by a nearness subgroup H can not be written two different decompositions of G by separate left (right) cosets [10]. In other words, if H is a nearness subgroup of a nearness group G, then G may be shown as a union of different non-discrete left (right) cosets of H in G. Also, it is given that Lagrange’s theorem does not work in the nearness subgroups as usual subgroups. Our purpose in this paper is to introduce normal nearness subgroups and quotient nearness groups. Besides which, it is given an example of a nearness group that has nearness subgroup but not normal nearness subgroup. Also, a criterion that satisfies the condition of being a normal subgroup is investigated. It is shown that the multiplication of the two right near-cosets (left near-cosets) is again a right near-coset (left near-coset) is valid in normal nearness subgroups under certain conditions. Moreover, examples of normal nearness subgroups and quotient nearness groups are given. © 2023 Taylor & Francis Group, LLC.
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