Galaxy groups and clusters and their brightest galaxies within the cosmic web

Our aim is to combine data on single galaxies, galaxy groups, their BGGs, and their location in the cosmic web, to determine classes of groups, and to obtain a better understanding of their properties and evolution. Data on groups and their BGGs are based on the Sloan Digital Sky Survey DR10 MAIN spectroscopic galaxy sample. We characterize the group environments by the luminosity-density field and their filament membership. We divide BGGs according to their star formation properties as quenched, and red and blue star-forming galaxies. We apply multidimensional Gaussian mixture modelling to divide groups based on their properties and environments. We analyse the offset of BGGs with respect to the group centre, and the relation between the stellar velocity dispersion of BGGs and the group velocity dispersions. We show that the groups in our sample can be divided into two main classes: high-luminosity rich groups and clusters, and low-luminosity poor groups with threshold luminosity $L = 15 \times 10^{10} h^{-2} L_{sun}$ and mass $M = 23 \times 10^{12} h^{-1} M_{sun}$. In rich clusters approximately 90% of the BGGs are red and quenched galaxies, while in poor groups only 40- 60$% of BGGs are red and quenched, and the rest of the BGGs are star-forming, either blue (20 - 40% of BGGs) or red (17% of BCGs). Rich groups and clusters are located in global high-density regions in filaments or filament outskirts, while poor groups reside everywhere in the cosmic web. Our results suggest that group and cluster properties are modulated by their location in the cosmic web, but the properties of their BGGs are mostly determined by processes within group or cluster dark matter halo. We emphasize the role of superclusters as a special environment for group growth.