Two purity theorems and the Grothendieck-Serre conjecture concerning principal $\mathbf G$-bundles

The main results of the paper are two purity theorems for reductive group schemes over regular local rings containing a field. Using these two theorems a well-known Grothendieck-Serre conjecture on principal bundles is reduced to the simply-connected case. We point out that the mentioned reduction is one of the major steps in the proof of the conjecture that the author published in another work.
Bibliography: 25 titles.