Let k be an algebraically closed field of prime characteristic p, G a finite group and P a p-subgroup of G . We investigate the relationship between the fusion system rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303416&_mathId=si1.gif&_user=111111111&_pii=S0021869316303416&_rdoc=1&_issn=00218693&md5=841aab88b1c39386fb5e6b8daa315f0e" title="Click to view the MathML source">FP(G)r hidden"> and the Brauer indecomposability of the Scott kG-module in the case that P is not necessarily abelian. We give an equivalent condition for Scott kG-module with vertex P to be Brauer indecomposable.