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Near set theory provides a formal basis for observation, comparison and classification of perceptual granules. In the near set approach, every perceptual granule is a set of objects that have their origin in the physical world. Objects that have, in some degree, affinities are considered perceptually near each other, i.e., objects with similar descriptions. In this paper, firstly we introduce the concept of near groups, near subgroups, near cosets, near invariant sub-groups, homomorphisms and isomorphisms of near groups in nearness approximation spaces. Then we give some properties of these near structures.