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Compared with the expectation in a semi-analytical model applied to the Millennium Simulation, the observed BCGs become under-massive\/under-luminous with decreasing redshift. We incorporate the uncertainties associated with cluster mass, redshift, and BCG stellar mass measurements into an analysis of a redshift-dependent BCG-cluster mass relation, <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     \n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"apj521919ieqn1.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>, and compare the observed relation to the model prediction. We estimate the average growth rate since <jats:italic>z<\/jats:italic> = 1.0 for BCGs hosted by clusters of <jats:italic>M<\/jats:italic>\n                  <jats:sub>200,<jats:italic>z<\/jats:italic>\n                  <\/jats:sub>\u00a0=\u00a010<jats:sup>13.8<\/jats:sup>\n                  <jats:italic>M<\/jats:italic>\n                  <jats:sub>\u2299<\/jats:sub>; at <jats:italic>z<\/jats:italic> = 1.0: <jats:italic>m<\/jats:italic>\n                  <jats:sub>*,BCG<\/jats:sub> appears to have grown by 0.13\u00a0\u00b1\u00a00.11 dex, in tension at the \u223c2.5<jats:italic>\u03c3<\/jats:italic> significance level with the 0.40 dex growth rate expected from the semi-analytic model. We show that the build-up of extended intracluster light after <jats:italic>z<\/jats:italic> = 1.0 may alleviate this tension in BCG growth rates.<\/jats:p>","DOI":"10.3847\/0004-637x\/816\/2\/98","type":"journal-article","created":{"date-parts":[[2016,1,15]],"date-time":"2016-01-15T00:13:00Z","timestamp":1452816780000},"page":"98","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":49,"title":["GALAXIES IN X-RAY SELECTED CLUSTERS AND GROUPS IN DARK ENERGY SURVEY DATA. I. 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