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Normal nearness subgroups

Authors
Öztürk, Mehmet AliTekin, ÖzlemJun, Young Bae
Issue Date
Jul-2023
Publisher
Taylor and Francis Ltd.
Keywords
Groups; near sets; nearness groups; nearness subgroups; normal nearness subgroups; quotient nearness groups; weak nearness approximation spaces
Citation
Communications in Algebra
Indexed
SCIE
SCOPUS
Journal Title
Communications in Algebra
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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