| Summary: | Evolution of galaxies is one of the most important topics in astronomy to understand how the universe has been evolving. In particular, galaxy groups are important because they are the observable equivalent of dark matter (DM) haloes, and thus offer a direct insight into the physics that has occurred in the DM haloes in the Universe up to the present day. Isolated galaxies are crucial for studying intrinsic and secular processes able to affect the structure, morphology, and dynamics of galaxies for obtaining clear relationships and correlations to be confronted with the model predictions. The main goal of this work is to characterize the GAMA G3Cv1 galaxy groups catalogue and the UNAM-KIAS catalogue of isolated galaxies by one of the most important statistical studies, the galaxy Luminosity Function (LF), that helps to constrain the models of formation and evolution of galaxies. LFs have been estimated for galaxies in groups and isolated galaxies. The LF for groups has been characterized by the physical properties of the groups (mass and velocity dispersion), the photometry (colour), the morphological type and eleven wavelengths from the far infra-red to the ultra violet. The LF estimated for the isolated galaxies is characterized by morphology and the colour in the five SDSS bands. The results obtained constrain more effectively the formation and evolution models of the universe than previous samples. The differences between both catalogues are presented in the conclusions. Additionally, the galaxy morphology is one of the no well understood problems in the galaxy evolution process to support the hierarchical model of formation of large objects. In this work, a classification based on the colour and concentration of light was considered. However, due to the low resolution of the images, the confidence of this classification was only ~60%.
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