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Environment is one of the key external drivers of the galaxies, while active galactic nucleus (AGN) is one of the key internal drivers. Both of them play fundamental roles in regulating the formation and evolution of galaxies. We explore the interrelationship between environment and AGN in SDSS. At a given stellar mass, the specific star formation rate distribution of the AGN host galaxies remains unchanged with over-density, with the peak of the distribution around the Green Valley. We show that, at a given stellar mass, the AGN fraction that has been commonly used in previous studies (defined as the number of AGNs relative to all galaxies including passive and star forming ones) does decrease with increasing over-density for satellites. This is largely due to the fact that the fraction of passive galaxies strongly depends on environment. In order to investigate the intrinsic correlation between AGN and environment, especially under the assumption that AGN feedback is responsible for star formation quenching, the AGN fraction should be defined as the number of AGNs relative to the star-forming galaxies only. With the new definition, we find little dependence of AGN fraction on over-density, central/satellite, and group halo mass. There is only marginal evidence that AGN may prefer denser regions, which is possibly due to more frequent interaction of galaxies or higher merger rate in groups. Our results support the scenario that internal secular evolution is the predominant mechanism of triggering AGN activity, while external environment related processes only play a minor role., Comment: Accepted for publication in MNRAS, submitted on June 4. 11 pages, 7 figures

We explore the interrelationships between the galaxy group halo mass and various observable group properties. We propose a simple scenario that describes the evolution of the central galaxies and their host dark matter halos. Star formation quenching is one key process in this scenario, which leads to the different assembly histories of blue groups (group with a blue central) and red groups (group with a red central). For blue groups, both the central galaxy and the halo continue to grow their mass. For red groups, the central galaxy has been quenched and its stellar mass remains about constant, while its halo continues to grow by merging smaller halos. From this simple scenario, we speculate about the driving properties that should strongly correlate with the group halo mass. We then apply the machine learning algorithm the Random Forest (RF) regressor to blue groups and red groups separately in the semianalytical model L-GALAXIES to explore these nonlinear multicorrelations and to verify the scenario as proposed above. Remarkably, the results given by the RF regressor are fully consistent with the prediction from our simple scenario and hence provide strong support for it. As a consequence, the group halo mass can be more accurately determined from observable galaxy properties by the RF regressor with a 50% reduction in error. A halo mass more accurately determined in this way also enables more accurate investigations on the galaxy-halo connection and other important related issues, including galactic conformity and the effect of halo assembly bias on galaxy assembly., Comment: Accepted for publication in The Astrophysical Journal, submitted on Feb 24. 16 pages, 6 figures. Grammar mistakes are corrected, results unchanged