On centers of \(2\)-blocks of Suzuki groups (Q1974164)

It is proved that the center of the principal block \(Z(kGe)\) of the Suzuki group \(G=Sz(q)\), where \(k\) is a field of characteristic 2, is isomorphic to the center of the Brauer corresponding block \(Z(kH)\), where \(H\) is the normalizer in \(G\) of a Sylow \(2\)-subgroup, but over a discrete valuation ring \(R\) of characteristic 0 whose residue field has characteristic 2, the center of the principal block \(Z(RGe)\) is not \(R\)-isomorphic to the center \(Z(RH)\) of the Brauer corresponding block.