| Active Galactic Nucleus (AGN) is a kind of extragalactic population with intense activities in the central nuclei. The main characteristic of AGN is the nuclear activities, and its energy comes from the central black hole accretion, which should have played an important role in the formation and evolution of galaxies. Clusters of galaxies are the largest gravitationally self-bound system in the universe, which is regarded as a laboratory for studying the evolutional process and the interaction with environment. The demographics of AGNs in clusters of galaxies will provide important clues for the growth of the supermassive black holes at the centers of cluster galaxies, the nature of AGN fueling, and the long-term impact of AGNs on the intracluster medium (ICM).The COSMOS Survey is one of the important observation plans of the Hubble Space Telescope, which covers two square degree regions near the equator. Using the samples of galaxy groups and member galaxies in the COSMOS deep field, we study the variation of AGN fraction in the galaxy groups with redshift on the basis of a sample of X-ray flux limited AGNs given by Brusa et al. (2010), which have been spectroscopically confirmed. According to evolutionary model of accretion processes, these AGNs with emission-line signatures are likely in the high-accretion phase of black hole growth. We take the sample of 211 X-ray selected galaxy groups with z< 1, provided by George et al. (2011), including group galaxies with F814W< 24.2 and a 3a detection in Ks band.A cross-identification of the AGN sample with the galaxies within X-ray selected galaxy groups is carried out. Only 27 AGNs are found in 26 galaxy groups, among which the vast majority (96%) are narrow-line AGNs. The AGN fraction for these 26 groups are derived, and a very weak increasing trend with redshift is found with a small linear correlation coefficiency. When the galaxy groups are devided in 10 subsamples with redshift interval of △z= 0.1, the group AGN fractions are generally less than 1%, and the trend becomes weaker. Additionally, After a separation of group galaxies into z< 0.5 and z> 0.5 subsamples, an increasing trend of AGN fraction with redshift seems to be more remarkable. As a comparison, we investigate the variation of AGN fraction in field with redshift, and a similar evolutionary trend is found, indicating that the environment of galaxy groups does not affect the frequence of the optically confirmed X-ray selected AGNs. |