Abstract
In 2019, Öztürk et al. [Gamma semigroups on weak nearness approximation spaces, Journal of the International Mathematical Virtual Institute 9 (2019) 53–72] defined the first algebraic structure on weak nearness approximation spaces which is the gamma semigroup. After this study, the view on the nearness of algebraic structures has completely changed. This view was first expressed in a previous study in 2021 [M. A. Öztürk, Nearness [Formula: see text]-algebras, Journal of Algebraic Hyperstructures and Logical Algebras 2 (2021) 73–84]. Our aim is to give the concept of modulo in the nearness group [Formula: see text] as in the nearness group [Formula: see text], where [Formula: see text] is the set of integers. Afterward, based on the concept of modulo in the nearness group [Formula: see text], the nearness cosets of the nearness group [Formula: see text] are constructed and its basic properties are examined. Lastly, it is seen that Lagrange theorem is not valid for the nearness subgroups as compared to the usual subgroups.
Published Version
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