Context. The construction of catalogues of galaxies and the a posteriori study of galaxy properties in relation to their environment have been hampered by scarce redshift information. The new 3-dimensional (3D) surveys permit small, faint, physically bound satellites to be distinguished from a background-projected galaxy population, giving a more comprehensive 3D picture of the surroundings. Aims. We aim to provide representative samples of isolated galaxies, isolated pairs, and isolated triplets for testing galaxy evolution and secular processes in low density regions of the local Universe, as well as to characterise their local and large-scale environments. Methods. We used spectroscopic data from the tenth data release of the Sloan Digital Sky Survey (SDSS-DR10) to automatically and homogeneously compile catalogues of 3702 isolated galaxies, 1240 isolated pairs, and 315 isolated triplets in the local Universe (z ≤ 0.080). To quantify the effects of their local and large-scale environments, we computed the projected density and the tidal strength for the brightest galaxy in each sample. Results. We find evidence of isolated pairs and isolated triplets that are physically bound at projected separations up to d ≤ 450?kpc with radial velocity difference Δν ≤ 160?km?s-1, where the effect of the companion typically accounts for more than 98% of the total tidal strength affecting the central galaxy. For galaxies in the catalogues, we provide their positions, redshifts, and degrees of relation with their physical and large-scale environments. The catalogues are publicly available to the scientific community. Conclusions. For isolated galaxies, isolated pairs, and isolated triplets, there is no difference in their degree of interaction with the large-scale structure (up to 5?Mpc), which may suggest that they have a common origin in their formation and evolution. We find that most of them belong to the outer parts of filaments, walls, and clusters, and generally differ from the void population of galaxies.
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